Class 12 Vector Algebra · Assertion Reason1 Marksscalar_projection

Class 12 Maths · Vector Algebra · Assertion Reason #30

Assertion (A): If (a − b) · (a + b) = 0 for nonzero vectors a,b, then a and b are perpendicular. Reason (R): The scalar projection of (1,3,1) onto (2,−3,6) is −1/7.

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

✅ Step-by-Step Solution

Final Answer: Option (D): A is false but R is true.

The hypothesis only gives |a| = |b|; a = b = i is a counterexample to perpendicularity. The projection is (2 − 9 + 6)/7 = −1/7.

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Class 12 Maths · Vector Algebra · Assertion Reason #30

✅ Step-by-Step Solution

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