Question

Assertion (A): Given two non-zero vectors `veca` and `vecb`. If `vecr` is another non-zero vector such that `vecr xx (veca + vecb) = vec0`. Then `vecr` is perpendicular to `veca xx vecb`.

Reason (R): The vector `(veca + vecb)` is perpendicular to the plane of `veca` and `vecb`.

Options

• Both (A) and (R) are true and (R) is the correct explanation of (A).

• Both (A) and (R) are true but (R) is not the correct explanation of (A).

• (A) is true but (R) is false.

• (A) is false but (R) is true.

Answer 1

(A) is true but (R) is false.

Explanation:

`vecr xx (veca + vecb) = vec0` 

⇒ `vecr` is parallel to `(veca + vecb)` and `(veca + vecb)` lies on the plane of `veca` and `vecb`.

So, `vecr` is parallel to the plane of `veca` and `vecb`

⇒ `vecr` is perpendicular to `(veca xx vecb)`.

So, Assertion is true.

But `(veca + vecb)` lies on the plane of `veca` and `vecb`, so `(veca + vecb)` is not perpendicular to the plane of `veca` and `vecb`.

Therefore, Reason is false.