The vectors ` vec P = a hat I + a hat j + 3 hat k)` and ` vec Q = a hat I - 2 hat j - hat kl` are peroendicular to each other. The positve value of (a) is.

Options

A. ` 3`
B. `2`
C. `1`
D. `0`

Answer

A

Explanation

For peroendicular vectors ` vec P . Vec Q =0`
` (a hat i+ a hat j+ 3 hat k) . ( a hat i- 2 hat j- hat k)=0`
or ` a^2 - 2 a - 3 =0`
` (a- 3) (a+ 1) = 0 ` so a = 3 or `-1`
So, (positive value of (a) is (3)`.