If the vectors `vec(P)=ahat(i) + ahat(j) + 3hat(k)` and `vec(Q)=ahat(i) -2hat(j) - hat(k)` are perpendicular to each other, then positive value of a is :

Options

A. 3
B. 2
C. 1
D. zero

Answer

A

Explanation

Here `vec(P)=ahati+ahatj +3hatk, vec(Q)=ahati-2hatj-hatk`
Dot product of `bot` r vector is zero i.e., `vec(P).vec(Q)=0`
`(ahati + ahatj +3hatk)-(ahati-2hatj-hatk)=0`
`a^(2)-2a-3=0`
a(a-2)=3
when a = 3 only then a - 2 is positive.