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(i) If vec(a)=hat(i)+2hat(j)-3hat(k) and...

(i) If `vec(a)=hat(i)+2hat(j)-3hat(k)` and `vec(b)=3hat(i)-hat(j)+2hat(k)`, show that `(vec(a)+vec(b))` is perpendicular to `(vec(A)-vec(b))`.
(ii) If `vec(a)=(5hat(i)-hat(j)-3 hat(k))` and `vec(b)=(hat(i)+3hat(j)-5hat(k))` then show that `(vec(a)+vec(b))` and `(vec(a)-vec(b))` are orthogonal.

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