Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) `vec(a)=hat(i) + 2 hat(j)+ 3 hat(k)` and `vec(b)=-3 hat(i)- 2 hat(j) + hat(k)` (ii) `vec(a)=(3 hat(i)+hat(j) + 4 hat(k))` and ` vec(b)= ( hat(i)- hat(j) + hat(k))` (iii) `vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j)` (iv)`vec(b)= 2 hat(i) and vec(b) = 3 hat(j).`

Answer

`6sqrt(5)` sq units (ii) `sqrt(42)` sq units (iii) `3sqrt(3)` sq units (iv) 6 sq units

Explanation

(iv) Area`=|vec(a) xx vec(b)|= |2 hat(i) xx 3 hat(j)| = |6(hat(i) xx hat(j))|=|6hat(k)|=6 " "[:' (hat(i) xx hat(j)) = hat(k)].`