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3d Geometry Mathematics Questions — 39+ MCQs & PYQs | ExamTest.live

Q: How many 3D Geometry questions are asked in Mathematics Mock Test - 5?

ExamTest.live has 39 3D Geometry questions from Mathematics Mock Test - 5, covering years 2026–2026.

3D Geometry — Mathematics Mock Test - 5(1–39 of 39)

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Q1mediummcqMathematicsMathematics Mock Test - 52026

15% accuracy

What is the perpendicular distance from the point (2, 3, 4) to the line \frac{x - 0}{1} = \frac{y - 0}{0} = \frac{z - 0}{0} ?

Q2mediummcqMathematicsMathematics Mock Test - 102026

9% accuracy

The lines x = p y + q, z = ry + s and x = p^{'} y + q^{'}, z = r^{'} y + s^{'} are perpendicular to each other, if:

Q3hardmcqMathematicsMathematics Mock Test - 102026

0% accuracy

The equation of a plane passing through the line of intersection of the planes x + 2 y + 3 z = 2 and x - y + z = 3 and at a distance \frac{2}{3} from the point (3, 1, - 1) is a x + b y + cz - 17 = 0 . The value of a + b + c - 17 is:

Q4mediummcqMathematicsMathematics Mock Test - 102026

9% accuracy

Let the line \frac{x - 1}{2} = \frac{y + 2}{- 3} = \frac{z - 3}{4} lie in the plane x - y + a z + b = 0 . The value of b - a is:

Q5mediummcqMathematicsMathematics Mock Test - 102026

0% accuracy

The triangle formed by the points A (0, 7, 10), B (- 1, 6, 6) and C (- 4, 9, 6) is:

Q6mediummcqMathematicsMathematics Mock Test - 102026

9% accuracy

The ratio in which the line segment joining the points A (4, 8, 10) and B (6, 10, - 8) is divided by the yz -plane is:

Q7mediummcqMathematicsMathematics Mock Test - 52026

0% accuracy

A straight line with direction cosines {0, 0, 1} is:

Q8mediummcqMathematicsMathematics Mock Test - 52026

50% accuracy

Find the image of the point (- 2, 1, 1) in the plane x + y + z = 0 .

Q9mediummcqMathematicsMathematics Mock Test - 52026

0% accuracy

Find the shortest distance between the lines \frac{x - 1}{- 1} = \frac{y - 2}{0} = \frac{z}{1} and \frac{x + 2}{1} = \frac{y}{1} = \frac{z}{0} .

Q10mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?

Q11mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

Determine the coordinates of the foot of the perpendicular drawn from the origin to the plane 4 x - 2 y + 3 z - 6 = 0 .

Q12mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

If \frac{x - 1}{l} = \frac{y - 2}{m} = \frac{z + 1}{n} is the equation of the line passing through (1, 2, - 1) and (- 1, 0, 1), then (l, m, n) is:

Q13mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

Find the Cartesian equation of the plane which passes through the point (5, 2, - 4) and is perpendicular to the line with direction ratios 2, 3, - 1 ?

Q14mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

Find the angle between the pair of lines \frac{x - 5}{3} = \frac{y + 2}{5} = \frac{z + 2}{4} and \frac{x - 1}{1} = \frac{y - 3}{1} = \frac{z - 3}{2} .

Q15mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

Determine the coordinates of the point where the line through the points A (2, 3, 2) and B (5, 1, 6) crosses the X Y -plane.

Q16mediummcqMathematicsMathematics Mock Test - 92026

0% accuracy

Which of the following is NOT a known factor to uniquely determine a plane?

Q17mediummcqMathematicsMathematics Mock Test - 42026

100% accuracy

The plane 2 x - 3 y + 6 z - 11 = 0 makes an angle sin^{- 1} (α) with the X-axis. The value of α is equal to:

Q18mediummcqMathematicsMathematics Mock Test - 42026

100% accuracy

Find the distance between the straight line \frac{x - 3}{1} = \frac{y - 4}{2} = \frac{z - 5}{1} and the plane x - y + z - 5 = 0 .

Q19mediummcqMathematicsMathematics Mock Test - 42026

100% accuracy

If the lines \frac{x - x _{1}}{a} = \frac{y - y _{1}}{b} = \frac{z - z _{1}}{c} and \frac{x - x _{2}}{p} = \frac{y - y _{2}}{q} = \frac{z - z _{2}}{r} lie on the same plane, then:

Q20mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

If a line has direction ratios ⟨ a + b, b + c, c + a ⟩, then what is the sum of the squares of its direction cosines?

Q21mediummcqMathematicsMathematics Mock Test - 22026

0% accuracy

The length of the perpendicular drawn from the origin to the plane 2 x - 3 y + 6 z - 42 = 0 is:

Q22mediummcqMathematicsMathematics Mock Test - 32026

What is the cosine of the angle between the planes x + y + z + 1 = 0 and 2 x - 2 y + 2 z + 1 = 0 ?

Q23mediummcqMathematicsMathematics Mock Test - 112026

The reflection of the origin in the plane P_{2} : 2 x + 3 y + 4 z + 5 = 0 is:

Q24mediummcqMathematicsMathematics Mock Test - 112026

Let P be the plane passing through the intersection of planes P_{1} : x + y + z - 6 = 0 and P_{2} : 2 x + 3 y + 4 z + 5 = 0 . If the plane P contains the origin, then the equation of the plane P is:

Q25mediummcqMathematicsMathematics Mock Test - 112026

The number of straight lines that are equally inclined to the three-dimensional coordinate axes is:

Q26mediummcqMathematicsMathematics Mock Test - 112026

If the coordinates of A and B are (1, 2, 3) and (7, 8, 7), then the projections of the line segment A B on the coordinate axes are:

Q27mediummcqMathematicsMathematics Mock Test - 112026

A line joining the points (1, 2, 0) and (4, 13, 5) is perpendicular to a plane. Then the coefficients of x, y and z in the equation of the plane are respectively:

Q28mediummcqMathematicsMathematics Mock Test - 112026

Consider the plane passing through the points A (2, 2, 1), B (3, 4, 2) and C (7, 0, 6) . What are the direction ratios of the normal to the plane?

Q29mediummcqMathematicsMathematics Mock Test - 112026

Consider a plane passing through the points A (2, 2, 1), B (3, 4, 2) and C (7, 0, 6) . Which one of the following points lies on this plane?

Q30mediummcqMathematicsMathematics Mock Test - 112026

Let L be a line that is perpendicular to the plane x - 3 y + 2 z = k and passes through the point (1, 2, - 2) . The point on the line L that is nearest to the y -axis is:

Q31mediummcqMathematicsMathematics Mock Test - 112026

Three vertices of a parallelogram A BC D are A (1, 2, 3), B (- 1, - 2, - 1) and C (2, 3, 2) . The coordinates of the fourth vertex D are:

Q32mediummcqMathematicsMathematics Mock Test - 82026

If the plane 2 x - y + z = 0 is parallel to the line \frac{2 x - 1}{2} = \frac{2 - y}{2} = \frac{z + 1}{a}, then the value of a is:

Q33mediummcqMathematicsMathematics Mock Test - 32026

The lines \frac{x + 3}{- 4} = \frac{y - 6}{3} = \frac{z}{2} and \frac{x + 2}{- 4} = \frac{y}{1} = \frac{z - 7}{1} are:

Q34mediummcqMathematicsMathematics Mock Test - 32026

The line with direction ratios 1, 0, - 1 is inclined with the z -axis at an angle of:

Q35mediummcqMathematicsMathematics Mock Test - 82026

Determine the direction cosines of the unit vector perpendicular to the plane r \cdot (2 \hat{i} - 6 \hat{j} - 3 \hat{k}) + 1 = 0 passing through the origin?

Q36mediummcqMathematicsMathematics Mock Test - 82026

Determine the vector equation for the line, given the Cartesian equation is \frac{x + 5}{3} = \frac{y - 7}{2} = \frac{z + 3}{2} ?

Q37mediummcqMathematicsMathematics Mock Test - 82026

Determine the vector equation of the plane passing through the intersection of the planes r \cdot (\hat{i} + \hat{j} + \hat{k}) = 6 and r \cdot (2 \hat{i} + 3 \hat{j} + 4 \hat{k}) = - 5, and through the point (1, 1, 1) ?

Q38mediummcqMathematicsMathematics Mock Test - 82026

If from a point P (a, b, c), perpendiculars P A and PB are drawn to the yz and z x planes respectively, then the equation of the plane O A B (where O is the origin) is:

Q39mediummcqMathematicsMathematics Mock Test - 82026

The ratio in which the plane x - 2 y + 3 z = 17 divides the line joining the points (- 2, 4, 7) and (3, - 5, 8) is:

Mathematics Mock Test - 5 3D Geometry — FAQ

How many 3D Geometry questions come in Mathematics Mock Test - 5?▼

Our database has 39 3D Geometry questions from Mathematics Mock Test - 5 covering 2026 to 2026.

What difficulty are Mathematics Mock Test - 5 3D Geometry questions?▼

The 39 Mathematics Mock Test - 5 3D Geometry questions include 0 easy, 38 medium and 1 hard level questions.

Where can I find more 3D Geometry questions for other exams?▼

Visit /tag/3d-geometry to see all 3D Geometry questions across all exams including Mathematics Mock Test - 11, AIEEE, Competitive Exam.

3D Geometry Questions

3D Geometry — Mathematics Mock Test - 5(1–39 of 39)

Mathematics Mock Test - 5 3D Geometry — FAQ