Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a+2b is collinear with c and b+3c is collinear with a - Mathematics MCQ AIEEE 2004 2026 | ExamTest.live

hardMCQAIEEE 20042026Mathematics

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Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a + 2 b is collinear with c and b + 3 c is collinear with a then a + 2 b + 6 c equals

Solution & Step-by-step Explanation

Given: a + 2 b = t_{1} c . b + 3 c = t_{2} a .From (1), a = t_{1} c - 2 b .Substitute this into (2): b + 3 c = t_{2} (t_{1} c - 2 b) b + 3 c = t_{1} t_{2} c - 2 t_{2} b b (1 + 2 t_{2}) + c (3 - t_{1} t_{2}) = 0 . Since b and c are non-collinear, their coefficients must be zero: 1 + 2 t_{2} = 0 \Rightarrow t_{2} = - 1/2 . 3 - t_{1} t_{2} = 0 \Rightarrow 3 - t_{1} (- 1/2) = 0 \Rightarrow 3 + t_{1} /2 = 0 \Rightarrow t_{1} = - 6 . Substituting t_{1} = - 6 in (1): a + 2 b = - 6 c a + 2 b + 6 c = 0 .

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Let a, b and c be three non-zero vectors such that no two of these are collinear. If the vector a + 2 b is collinear with c and b + 3 c is collinear with a then a + 2 b + 6 c equals

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λ b

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