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)=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 .

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)) .

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.

vec(a)=hatj-hatk and vec( c )=hati-hatj-hatk . The vector vec(b) is such that vec(a) xx vec(b)+vec( c )=0 and vec(a)*vec(b)=3 then vec(b) = ………..

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)=hati+hatj+hatk,vec(b)=hati-hatj+hatk and vec( c )=hati+2hatj-hatk then the value of |{:(vec(a).vec(b),vec(a).vec(b),vec(a).vec( c )),(vec(b).vec(a),vec(b).vec(a),vec(b).vec( c )),(vec( c ).vec(a),vec( c ).vec(b),vec( c ).vec( c )):}| is .............

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 )) .