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.

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 any vectors, then which the following is equal to vec(a) xx vec(b) +vec(b)xx vec(c ) + vec(c ) xx vec(a) ?

The vectors vec(a) " and " vec(b) are non-collinear. Find for what value of x, the vectors vec(c)=(x-7)vec(a)+2vec(b) "and " vec(d)=(2x+1)vec(a)-vec(b) are collinear.

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

Show that the vectors |vec(a)xxvec(b)|^(2)=|(vec(a).vec(a)" "vec(a).vec(b)),(vec(a).vec(b)" "vec(b).vec(b))|

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.

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

If vec(a), vec(b) " and " vec(c) are unit vectors satisfying abs(vec(a)-vec(b))^(2)+abs(vec(b)-vec(c))^(2)+abs(vec(c)-vec(a))^(2)=9, " then " abs(2vec(a)+5vec(b)+5vec(c)) is -

If vec(a) , vec(b) and vec (c ) are three unit vectors such that vec(a).vec(b) = vec(a).vec (c )=0 and angle between vec(b) and vec (c ) is pi/6 , prove that , vec (a) = pm 2 ( vec(b) xx vec(c ))