Assertion (A): Let `vec(a) = a_(1) vec(i) + a_(2) vec(j) + a_(3) vec(k)`. Then identity `|vec(a) xx vec(i)|^(2) + |vec(a) xx vec(j)|^(2) + |vec(a) xx vec(k)|^(2) =2|vec(a)|^(2)` holds for `vec(a)`.
Reason (R ): `vec(a) xx vec(i) = a_(3) vec(j)- a_(2) vec(k), vec(a) xx vec(j) = a_(1) vec(k) - a_(3) vec(i), vec(a) xx vec(k)= a_(2) vec(i) - a_(1) vec(j)` Which of the following is correct ?

Options

A. Both (A) and (R ) are true and (R ) is the correct explanation of (A)
B. Both (A) and (R ) are true and (R ) is not the correct explanation of (A)
C. (A) is true, (R ) is false
D. (A) is false, (R ) is true

Answer

A