The vectors `vec(a), vec(b),vec(c )` are of same magnitude and taken pariwise , they contain equal angles. If `vec(a) = hat(i) +hat(j) , vec(b) = hat(j) + hat(k) ` then the vector `vec(c )` =

The vectors vec a,vec b,vec c are of the same length and pairwise form equal angles.If vec a=hat i+hat j and vec b=hat j+hat k then vec c may be :

If vec(a) = hat(i) + hat(j) + hat(k), vec(a).vec(b) =1 and vec(a) xx vec(b) = hat(j)-hat(k) , then the vector vec(b) is

Find the scalar and vector components of vec(a) in the direction of vec(b) where vec(a) = hat (i) + hat(j) and vec(b) = hat (j) + hat (k)

Find vec(c) , when vec(a) xx vec(c) = vec(b) and vec(a).vec(c) =3 where vec(a) = hat(i) + hat(j) + hat(k) and vec(b) = hat(j) - hat(k)

Find a unit vector in the direction of vec a- 2 vec b+ 3 vec c if vec a= hat i+ hat j , vec b= hat j+ hat k and vec c= vec i+ vec k .

Vectors vec a , vec b , vec c and vec d are given by vec a= hat i+ hat j+ hat k , vec b= 2 hat i+ 3 hat j , vec c= 3 hat i+ 5 hat j- 2 hat k and vec d= - hat j+ hat k . Show that the vectors vec b- vec a and vec d- vec c are parallel and find the ratio of their lengths.

Find the projection of vector (vec(b)+vec(c )) on vector vec(a) where vec(a) = hat (i) + 2 hat (j) + hat (k) , vec(b) = hat (i) + 3 hat (j) + hat (k) and vec c = hat (i) + hat (k)

Given the three vectors vec(a) = - 2hati + hat(j) + hat(k), vec(b) = hat(i) + 5hat(j) and vec(c) = 4hat(i) + 4hat(j) - 2hat(k) . The projection of the vector 3vec(a) - 2vec(b) on the vector vec(c) is