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CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Q201 Markscollinearity

CBSE Class 12 Mathematics 2026 Supplementary Paper 65/7/1 · Question 20 (Vector Algebra)

Assertion A. Points A=(6,−7,0), B=(16,−19,−4), C=(1,−1,2) are collinear. Reason R. Three points are collinear when C is the midpoint of AB.

(A) Both statements are true and R correctly explains A.
(B) Both statements are true but R does not correctly explain A.
(C) A is true and R is false.
(D) A is false and R is true.

✅ Step-by-Step Solution

Final Answer: Both statements are true but R does not correctly explain A.

AB=(10,−12,−4) and AC=(−5,6,2)=−AB/2, so A is true. The midpoint criterion is sufficient, hence R is true, but C is not the midpoint of AB and this reason does not explain this instance.

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