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

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

For vectors vec(a),vec(b) and vec( c ),vec(a).vec(b)=vec(a).vec( c ) and vec(a)xx vec(b)=vec(a)xx vec( c ),vec(a) ne vec(0) then show that vec(b)=vec( c ) .

The position vectors of four points A, B, C and D in the plane are vec(a),vec(b),vec( c ) and vec(d) . If (vec(a)-vec(d)).(vec(b)-vec( c ))=(vec(b)-vec(d)).(vec( c )-vec(a))=0 then D is a ………………is DeltaABC .

For three vectors vec(a),vec(b) and vec( c ),vec(a)+vec(b)+vec( c )=vec(0)|vec(a)|=3,|vec(b)|=4,|vec( c )|=5 , then evaluate 2(vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a)) .

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)=3hati-hatj+2hatk,vec(b)=hati-3hatk and vec( c )=hati+2hatj then find (i) vec(a).vec(b) (ii) (vec(a)+vec(b)).vec( c ) (iii) (vec(a)-vec(b)).(vec(b)-vec( c )) (iv) (vec(a)+2vec(b)).vec(b) (v) (vec(a)-3vec( c )).(2vec(a)+vec(b))

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

Let vec(a),vec(b) and vec( c ) be three unit vectors such that vec(a),+vec(b)+vec( c )=vec(0) . If lambda=vec(a)*vec(b)+vec(b)*vec( c )+vec( c )*vec(a) and vec(d)=vec(a)xx vec(b)+vec(b)xx vec( c )+vec( c )xx vec(a) then the ordered pair (lambda, vec(d)) is equal to :

(vec(a)xx vec(b))xx vec( c )=vec(a)xx(vec(b)xx vec( c )) . If vec(a)*vec( c ) ……………