Question

If the vectors `2hat(i)-3hat(j)+5hat(k)` and `3hat(i)+ahat(j)-2hat(k)` are perpendicular, then what is the value of `a` ?

Answer 1

`a = -4/3`

Explanation:

`2hat(i)-3hat(j)+5hat(k)` and `3hat(i)+ahat(j)-2hat(k)` are perpendicular if and only if their dot product is `0`.

`(2hat(i)-3hat(j)+5hat(k)).(3hat(i)+ahat(j)-2hat(k)) = 6-3a-10`

`color(white)((2hat(i)-3hat(j)+5hat(k)).(3hat(i)+ahat(j)-2hat(k))) = -3a-4`

So we require:

`0 = -3a-4`

Hence:

`a = -4/3`