Let ` vec u , vec v` and ` vec w` be vector such ` vec u+ vec v+ vec w= vec0` . If `| vec u|=3,| vec v|=4` and `| vec w|=5,` then find ` vec u . vec v+ vec v . vec w+ vec w . vec u` .

Let vec u ,\ vec v\ a n d\ vec w be vector such vec u+ vec v+ vec w=0.\ if | vec u|=3,\ | vec v|=4\ a n d\ | vec w|=5, then find vec udot vec vdot+ vec vdot vec w+ vec wdot vec udot

Let vec u , vec v and vec w be vectors such that vec u+ vec v+ vec w=0. If | vec u|=3,| vec v|=4 and | vec w|=5, then vec u. vec v+ vec v.vec w+ vec w.vec u is a. 47 b. -25 c. 0 d. 25

Let vec u and vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec v . Find the value of [ vec u \ vec v \ vec w] .

Vector vec a , vec b and vec c are such that vec a+ vec b+ vec c= vec0 and |a|=3,| vec b|=5 and | vec c|=7. Find the angle between vec a and vec b .

A vector vec d is equally inclined to three vectors vec a= hat i+ hat j+ hat k , vec b=2 hat i+ hat ja n d vec c=3 hat j-2 hat kdot Let vec x , vec y ,a n d vec z be three vectors in the plane of vec a , vec b ; vec b , vec c ; vec c , vec a , respectively. Then a. vec x. vec d=-1 b. vec y. vec d=1 c. vec z. vec d=0 d. vec r. vec d=0,w h e r e vec r=lambda vec x+mu vec y+delta vec z

If vec u , vec v and vec w are three non-coplanar vectors, then prove that ( vec u+ vec v- vec w) . [ [( vec u- vec v)xx( vec v- vec w)]]= vec u . vec v xx vec w

vec a , vec b , vec c are unit vectors such that vec a+ vec b+ vec c=0. then find the value of vec a. vec b+ vec b.vec c+ vec c. vec a

vec a , vec b , vec c are three vectors such that |vec a | = 5 | vec b | =8, |vec c | = 3 if vec a + vec b + vec c = 8 hati+ 6hatj , find the value of vec a , vec b +vec b .vec c + vec c .vec a

Let vec ua n d vec v be unit vectors such that vec uxx vec v+ vec u= vec w and vec wxx vec u= vec vdot Find the value of [ vec u vec v vec w]dot

If vec u , vec v and vec w are three non-cop0lanar vectors, then prove that ( vec u+ vec v- vec w)dot [( vec u- vec v)xx( vec v- vec w)] = vec u dot (vec v xx vec w)