Show that `(vec(a)-vec(b))xx(vec(a)+vec(b))=2 (vec(a)xxvec(b))`.

Find |vec(a)| and |vec(b)| , if (vec(a)+vec(b)).(vec(a)-vec(b))=8 and |vec(a)|=8|vec(b)| .

Find |vec(b)| , if (vec(a) + vec(b)).(vec(a) -vec(b)) = 8 and |vec(a)| = 8|vec(b)|

Prove that [vec(a),vec(b),vec( c) +vec(d)]=[vec(a),vec(b),vec( c)] +[vec(a),vec(b),vec(d)] .

If vec(a) = 2hat(i) - 3hat(j) + 4hat(k), vec(b) = hat(i) + 2hat(j) - 3hat(k) and vec(c ) = 3hat(i) + 4hat(j) - hat(k) , then find vec(a).(vec(b) xx vec(c )) and (vec(a) xx vec(b)).vec(c ) . Is, vec(a).(vec(b) xx vec(c )) = (vec(a) xx vec(b)).vec(c ) ?

If vec(a), vec(b), vec(c ) are unit vectors such that vec(a) + vec(b) + vec(c )= vec(0), " then " vec(a).vec(b) + vec(b).vec(c ) + vec(c ).vec(a) =

If vec(a),vec(b) and vec(c) are unit vectors such that vec(a)+vec(b)+vec(c)=0 , then 3vec(a).vec(b)+2vec(b).vec(c)+vec(c).vec(a)=

If |vec(a) + vec(b)| = |vec(a) - vec(b)| then

Prove that [vec(a)+vec(b),vec(b)+vec( c) , vec( c) +vec(a)] =2 [vec(a),vec(b),vec(c )] .

If vec(a)=i-2 j + 3k, vec(b) is a vector such that vec(a).vec(b)= |vec(b)|^(2) |vec(a)-vec(b)|= sqrt7 , then |vec(b)| = ________