If `vec(a)=hati+2hatj-3hatk` and `vec(b)=3hati-hatj+2hatk` then show that `(vec(a)+vec(b))` is a perpendicular to the vector `vec(a)-vec(b)`.

If vec(a)=hati+hatj+2hatk and vec(b)=3hati+2hatj-hatk then find vec(a)+3vec(b).(2vec(a)-vec(b)) .

If vec(a)=5hati-hatj-3hatk and vec(b)=hati+3hatj-5hatk , then show that the vectors vec(a)+vec(b) and vec(a)-vec(b) are perpendicualr.

If vec(a)=2hati+hatj+x hatk and vec(b)=hati+hatj-hatk then the minimum area of a parallelogram formed by the vectors vec(a) and vec(b) is ………….

vec(a)=3hati+2hatj+9hatk and vec(b)=hati+p hatj+3hatk . If the vector vec(a) and vec(b) are parallel then find the value of P.

If vec(a)=5hati-hatj+7hatk and vec(b)=hati-hatj+lambda hatk . If vec(a)+vec(b) and vec(a)-vec(b) are perpendicualr to each other then find the value of lambda .

vec(a)=lambda hati+3hatj+2hatk,vec(b)=hati-hatj+3hatk . If vec(a) and vec(b) are perpendicular to each other then find the value of lambda .

For given vectors vec(a)=3hati+4hatj-5hatk and vec(b)=2hati+hatj find the unit vectors in the direction of the vector vec(a)+2vec(b) .

If vec(a)=2hati+hatj+3hatk,vec(b)=-hati+2hatj+hatk and vec( c )=3hati+hatj+2hatk then find vec(a).(vec(b)xx vec( c )) .