Find the unit vectors perpendicular to both `vec(a)` and `vec(b)` when
(i) `vec(a) = 3 hat(i)+hat(j)-2 hat(k)` and `vec(b)= 2 hat(i) + 3 hat(j) - hat(k)`
(ii) `vec(a) = hat(i) - 2 hat(j) + 3 hat(k)` and `vec(b)= hat(i) +2hat(j) - hat(k)`
(iii) `vec(a) = hat(i) + 3 hat(j) - 2 hat (k)` and `vec(b)= -hat(i) + 3 hat(k)`
(iv) `vec(a) = 4 hat(i) + 2 hat(j)-hat(k) ` and `vec(b) = hat(i) + 4 hat(j) - hat(k)`

Answer

`(i) pm1/(5sqrt(3))(5hat(i)-hat(j)+7 hat(k)) " "(ii) pm1/(sqrt(3))(-hat(i)+hat(j)+ hat(k))`
(iii)`pm1/sqrt(3)(-hat(i)+hat(j)+hat(k)) " " (iv)pm 1/sqrt(209)(2hat(i)+3 hat(j)+14 hat(k))`

Explanation

Required vector`=(pm(vec(a) xx vec(b)))/(|vec(a) xx vec(b)|)`.