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Study the Assertion and Reason and choose the correct option.
(a⃗ + b⃗) · (b⃗ - a⃗) = 2 (a² + b²)
Assertion: $(\vec{a} + \vec{b}) \cdot (\vec{b} - \vec{a}) = 2 (a^2 + b^2)$
Reason: Dot product of any two vectors is commutative.
- (a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
- (b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- (c)Assertion is true and Reason is false.
- (d)Assertion is false and Reason is true.
Answer
Answer
Correct option: (d)
Answer: (d) Assertion is false and Reason is true.
$(\vec a+\vec b)\cdot(\vec b-\vec a)=\vec a\cdot\vec b-a^2+b^2-\vec b\cdot\vec a=b^2-a^2$ (using commutativity), which is not $2(a^2+b^2)$.