If `vec(a)=2hat(i)+5hat(j)-2hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k)`, then find
(i) `vec(a)+vec(b) " and " 2vec(a)-3vec(b) " " (ii)abs(vec(a)+vec(b)) " and " abs(vec(a)-2vec(b))`
(iii) a unit vector in the direction `(vec(a)+vec(b))`
(iv) vector and scalar components of the vector `(2vec(a)-3vec(b))` along the coordinate axes.

Answer

(i) ` hat(i)+13hat(j)-7hat(k)`
(ii) `sqrt(65)`
(iii) `(3hat(i)+4hat(j)-hat(k))/(sqrt(26))`