`ABCDE` is a pentagon. Prove that the resultant of forces `vec (AB), vec(AE), vec(BC), vec(DC), vec(ED) and vec(AC)` is `3vec(AC)`.

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

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

Prove that 3vec(OD)+vec(DA)+vec(DB)+vec(DC) is equal to vec(OA)+vec(OB)+vec(OC) .

The angle between vecP and the resultant of ( vec P + vec Q) and ( vec P - vec Q) is

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

If the vectors vec(a), vec(b) and vec(c ) are coplanar, prove that the vectors vec(a) + vec(b), vec(b) + vec(c ) and vec(c )+vec(a) are also coplanar.

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)| = 3, |vec(b) = 4 and |vec(a) + vec(b)| = 1 , then |vec(a) - vec(b)| =