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Vectors Questions

Practice 82 Vectors questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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82
Total Questions
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12
Easy
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61
Medium
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9
Hard
Practice by Exam:Mathematics(59)Physics(17)Biology(5)Zoology(1)

About vectors — practice questions, PYQs & concepts

vectors is a frequently-tested topic on Mathematics, Physics, Biology. ExamTest.live currently lists 82 vectors questions spanning previous-year papers from 2026 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

vectors weight in competitive exams

Across our vectors question bank, the largest sources are Mathematics (59), Physics (17), Biology (5) and Zoology (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 12 easy vectors questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Vectors Questions(1–82 of 82)

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Q1mediummcqMathematicsMathematics Mock Test - 62026
17% accuracy
Find the area of the parallelogram whose adjacent sides are given by the vectors and .
Q2mediummcqMathematicsMathematics Mock Test - 62026
4% accuracy
The equation of a plane passing through the point with position vector and perpendicular to vector is:
Q3mediummcqMathematicsMathematics Mock Test - 62026
0% accuracy
The vector component of along is:
Q4mediummcqMathematicsMathematics Mock Test - 62026
13% accuracy
Find a vector in the direction of vector that has a magnitude of units.
Q5mediummcqMathematicsMathematics Mock Test - 52026
15% accuracy
What is the perpendicular distance from the point to the line ?
Q6mediummcqMathematicsMathematics Mock Test - 102026
27% accuracy
For all real , the vectors and make an obtuse angle with each other. Then the value of must satisfy:
Q7mediummcqMathematicsMathematics Mock Test - 12026
9% accuracy
If the angle between and is and the projection of in the direction of is , then is:
Q8mediummcqMathematicsMathematics Mock Test - 102026
18% accuracy
A unit vector is coplanar to the vectors and and perpendicular to the vector . It is:
Q9mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
A straight line with direction cosines is:
Q10mediummcqMathematicsMathematics Mock Test - 52026
50% accuracy
Suppose and . If is a unit vector, then the maximum value of the scalar triple product is:
Q11mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
Find the projection of the vector on the vector .
Q12easymcqPhysicsAIEEE 20042026
0% accuracy
A force is applied over a particle which displaces it from its origin to the point . The work done on the particle in joules is:
Q13easymcqPhysicsAIEEE 20042026
0% accuracy
If , then the angle between and is:
Q14mediummcqMathematicsAIEEE 20072026
0% accuracy
If a line makes an angle of with the positive directions of each of -axis and -axis, then the angle that the line makes with the positive direction of the -axis is:
Q15mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
The vectors and are the sides of a triangle . The length of the median through is:
Q16hardmcqMathematicsAIEEE 20042026
0% accuracy
Let and be non-zero vectors such that If is the acute angle between the vectors and then equals
Q17hardmcqMathematicsAIEEE 20042026
0% accuracy
Let and be three non-zero vectors such that no two of these are collinear. If the vector is collinear with and is collinear with then equals
Q18hardmcqMathematicsAIEEE 20042026
0% accuracy
A particle is acted upon by constant forces and which displace it from a point to the point The work done in standard units by the forces is given by
Q19hardmcqMathematicsAIEEE 20042026
0% accuracy
Let be such that If the projection along is equal to that of along and are perpendicular to each other then equals
Q20hardmcqMathematicsAIEEE 20042026
0% accuracy
If are non-coplanar vectors and is a real number, then the vectors and are non-coplanar for
Q21mediummcqMathematicsAIEEE 20072026
0% accuracy
Let , and . If the vector lies in the plane of and , then equals:
Q22mediummcqMathematicsAIEEE 20072026
0% accuracy
If and are unit vectors and is the acute angle between them, then is a unit vector for:
Q23mediummcqMathematicsAIEEE 20062026
0% accuracy
The values of for which the points with position vectors , and respectively are the vertices of a right-angled triangle with are:
Q24mediummcqMathematicsAIEEE 20072026
100% accuracy
The resultant of two forces and is a force of . If the direction of force were reversed, the resultant would be . The value of is:
Q25mediummcqMathematicsAIEEE 20062026
0% accuracy
is a triangle, right-angled at . The resultant of the forces acting along and with magnitudes and respectively is a force along , where is the foot of the perpendicular from onto . The magnitude of the resultant is:
Q26mediummcqMathematicsAIEEE 20062026
0% accuracy
If , where and are any three vectors such that and , then and are:
Q27mediummcqMathematicsAIEEE 20062026
0% accuracy
A particle has two velocities of equal magnitude inclined to each other at an angle . If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then is:
Q28mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The magnitude of the projection of the vector on the vector perpendicular to the plane containing the vectors and is:
Q29mediummcqMathematicsMathematics Mock Test - 42026
100% accuracy
The vector is coplanar with:
Q30mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If , and are such that is perpendicular to , then determine the value of ?
Q31mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
A unit vector makes angle with , with and an acute angle with .I. The value of is .II. The components of are .Which of the above statement(s) is/are correct?
Q32mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If the vertices of a triangle are , , respectively, then determine .
Q33mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
In a triangle , , , , then the projection of the on is equal to:
Q34mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If and then the component of along is:
Q35mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
The vectors and are such that form a right-handed system. Then is:
Q36mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
Let be distinct non-negative numbers. If the vectors , and lie in a plane, then is:
Q37easymcqMathematicsAIEEE2026
If the vectors , and are mutually orthogonal, then
Q38mediummcqMathematicsMathematics Mock Test - 32026
The projection of a vector on another vector is:
Q39hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
If and , then the value of is:
Q40hardmcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The vectors and are not perpendicular and and are two vectors satisfying: and . Then the vector is equal to:
Q41mediummcqMathematicsAIEEE 20122026
Let and be two unit vectors. If the vectors and are perpendicular to each other, then the angle between and is:
Q42mediummcqMathematicsAIEEE 20122026
Let be a parallelogram such that , and be an acute angle. If is the vector that coincides with the altitude directed from the vertex to the side , then is given by:
Q43mediummcqMathematicsJEE Main2026
If the vectors and are the sides of a triangle , then the length of the median through is:
Q44mediummcqMathematicsMathematics Mock Test - 82026
Which of the following is true?
Q45mediummcqMathematicsMathematics Mock Test - 82026
Determine and , if and ?
Q46mediummcqMathematicsMathematics Mock Test - 82026
The number of vectors of unit length perpendicular to vectors and is:
Q47mediummcqMathematicsMathematics Mock Test - 32026
If and , then what is the position vector of the bisector of ?
Q48mediummcqMathematicsMathematics Mock Test - 32026
Given , , and where and . Then is:
Q49mediummcqMathematicsMathematics Mock Test - 112026
The unit vector perpendicular to line (DRs: ) and the normal to the plane is:
Q50mediummcqMathematicsAIEEE 20092026
The projections of a vector on the three coordinate axis are respectively. The direction cosines of the vector are:
Q51easymcqBiologyNEET (UG) 20182026
Which of the following is commonly used as a vector for introducing a fragment in human lymphocytes?
Q52mediummcqPhysicsNEET 20232026
A football player is moving southward and suddenly turns eastward with the same speed to avoid an opponent. The force that acts on the player while turning is:
Q53easymcqZoologyNEET 2024 R1@NUM: 1532026
The "Ti plasmid" of Agrobacterium tumefaciens stands for:
Q54mediummcqPhysicsAIEEE2026
A particle is moving eastwards with a velocity of . In the velocity changes to northwards. The average acceleration in this time is:
Q55mediummcqMathematicsAIEEE-CBSE-ENG-032026
If and vectors , and are non-coplanar, then the product equals:
Q56mediummcqMathematicsAIEEE-CBSE-ENG-032026
A tetrahedron has vertices at , , and . Then the angle between the faces and will be:
Q57mediummcqMathematicsAIEEE-CBSE-ENG-032026
are 3 vectors, such that , , then is equal to:
Q58mediummcqMathematicsAIEEE-CBSE-ENG-032026
If and are three non-coplanar vectors, then equals:
Q59mediummcqMathematicsAIEEE-CBSE-ENG-032026
A particle acted on by constant forces and is displaced from the point to the point . The total work done by the forces is:
Q60mediummcqMathematicsAIEEE-CBSE-ENG-032026
Let , and . If is a unit vector such that and , then is equal to:
Q61hardmcqPhysicsAIEEE 20032026
Three charges , and are placed as shown in the figure. ( at origin, at , at ). The -component of the force on is proportional to:
image
Q62mediummcqMathematicsAIEEE2026
The vector lies in the plane of the vectors and and bisects the angle between and . Then which one of the following gives possible values of and ?
Q63mediummcqMathematicsAIEEE2026
The non-zero vectors and are related by and . Then the angle between and is:
Q64mediummcqPhysicsAIEEE 20092026
A particle has an initial velocity and an acceleration of . Its speed after is:
Q65mediummcqMathematicsAIEEE 20092026
Let be non-coplanar vectors and are real numbers, then the equality holds for:
Q66mediummcqMathematicsAIEEE2026
Let and . Then vector satisfying and is:
Q67mediummcqMathematicsAIEEE-CBSE-ENG-032026
Consider points and with position vectors , , and respectively. Then is a:
Q68mediummcqPhysicsPhysics
0% accuracy
If a vector 2î + 3ĵ + 8 is perpendicular to the vector 4ĵ - 4î + α, then the value of α is :
Q69mediummcqPhysicsPhysics
0% accuracy
image
Q70mediummcqPhysicsPhysics
If a vector 2î + 3ĵ + 8 is perpendicular to the vector 4ĵ - 4î + α , then the value of α is :
Q71mediummcqPhysicsPhysics
If the angle between the vectors
Q72easymcqPhysicsPhysics
A particle starting from the origin moves in a straight line in the plane. Its coordinates at a later time are . The path of the particle makes with the -axis an angle of:
Q73easymcqPhysicsPhysics
and are two vectors and is the angle between them, if , the value of is:
Q74easymcqPhysicsPhysics
If is the force acting on a particle having position vector and be the torque of this force about the origin, then:
Q75easymcqPhysicsPhysics
Six vectors, through have the magnitudes and directions indicated in the figure. Which of the following statements is true?
image
Q76easymcqBiologyBiology
In genetic engineering, the antibiotics are used:
Q77mediummcqBiologyBiology
Which one of the following is a case of wrong matching?
Q78mediummcqBiologyBiology
The figure below is the diagrammatic representation of the E. coli vector pBR322. Which one of the given options correctly identifies its certain component(s)?
image
Q79easymcqPhysicsPhysics
A particle has initial velocity and acceleration . The magnitude of velocity after seconds will be:
Q80mediummcqBiologyBiology
Which vector can clone only a small fragment of DNA?
Q81hardmcqPhysicsPhysics
If vectors and are functions of time, then the value of at which they are orthogonal to each other is:
Q82easymcqPhysicsPhysics
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:

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Vectors questions are commonly asked in Mathematics, Physics, Biology, Zoology. You can filter by exam using the links above.
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Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.