Question

Assertion: `(veca + vecb)^2 + (vecb - veca)^2 = 2(a^2 + b^2)`

Reason: Dot product of any two vectors is commutative.

Options

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Assertion is false and Reason is true.

Answer 1

Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

Explanation:

Assertion: `(veca + vecb)^2 + (vecb - veca)^2`

`|veca|^2 + |vecb|^2 + 2veca * vecb + |vecb|^2 + |veca|^2 - 2vecb * veca`

= 2a² + 2b²

= 2(a² + b²)

∴ Assertion is true.

Reason: Dot product of any two vectors is commutative.

`veca * vecb = vecb * veca`

It is true.