Three non-zero vectors `vec(a), vec(b), vec(c)` are such that no two of them are collinear. If the vector `(vec(a)+vec(b))` is collinear with the vector `vec(c)` and the vector `(vec(b)+vec(c))` is collinear with vector `vec(a)`, then prove that `(vec(a)+vec(b)+vec(c))` is a null vector.

If vec a , vec b and vec c are three non-zero vectors, no two of which are collinear, vec a+2 vec b is collinear with vec c and vec b+3 vec c is collinear with vec a , then find the value of | vec a+2 vec b+6 vec c| .

Show that the vector vec(a) is perpendicular to the vector vec(b) - (vec(a).vec(b))/(|vec(a)|^(2))vec(a)

If vec(a) , vec(b)and vec(a) xx vec(b) are three unit vectors , find the angles beween the vectors vec(a) and vec(b)

Let vec(a), vec(b) and vec(c) be three non-zero vectors such that no two of them are collinear and (vec(a) xx vec(b)) xx vec(c) = (1)/(3) |vec(b)||vec(c)| vec(a) . If theta is the angle between vector vec(b) and vec(c) , then a value of sin theta is

For the vector vec(a) and vec (b) if |vec(a) + vec(b)| = |vec(a) - vec(b)| , show that vec(a) and vec (b) are perpendicular

Given three vectors vec a , vec b ,a n d vec c two of which are non-collinear. Further if ( vec a+ vec b) is collinear with vec c ,( vec b+ vec c) is collinear with vec a ,| vec a|=| vec b|=| vec c|=sqrt(2)dot Find the value of vec a. vec b+ vec b. vec c+ vec c. vec a a. 3 b. -3 c. 0 d. cannot be evaluated

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 ) =

If vec(x), vec(y), vec(z) are three vectors, show that the points having positive vectors 7vec(x) - vec(z), vec(x) + 2vec(y) + 3vec(z) and -2vec(x) + 3vec(y) + 5vec(z) are collinear

If vec(a), vec(b), vec(c) are three given vectors, show that the points having vectors 7vec(a)-vec(c), vec(a)+2vec(b) " and " -2vec(a)+3vec(b)+0.5vec(c) are collinear.

For non-zero vectors vec(a) and vec(b), " if " |vec(a) + vec(b)| lt |vec(a) - vec(b)| , then vec(a) and vec(b) are-