Let `vec(a) and vec(b)` be the position vectors of A and B respectively. If C is the point `3 vec(a)-2vec(b)`, then which one of the following is correct?

Let vec(a).vec(b) and vec(c ) be the position vectors of points A,B and C, respectively. Under which one of the following conditions are the points A, B and C collinear?

Let vec a and vec b be the position vectors of the points (3,-5) and (m,4) respectively. Find m if the vectors vec a and vec b are collinear.

If vec(a)xx vec(b) = vec(c) and vec(b) xx vec(c) = vec(a) , then which one of the following is correct?

If vec(a) and vec(b) are the position vectors of vec(A) and vec(B) respectively, then find the position vector of a point vec(C) and vec(BA) produced such that vec(BC) = 1.5 vec(BA) . Also, it is shown by graphically.

If vec(a),vec(b),vec(c) are the position vectors of the points A, B, C respectively such that 3vec(a)+5vec(b)=8vec(c) then find the ratio in which C divides AB.

If vec(a) and vec(b) are position vectors of the points A and B respectively, then what is the position vector of a point C on AB produced such that vec(AC) = vec(2AB) ?

Let vec(a).vec(b) and vec(c ) be three mutually perpendicular vectors each of unit magnitude. If vec(A) = vec(a) + vec(b) + vec(c ),  vec(B) = vec(a)- vec(b) + vec(c ) and vec(C ) = vec(a) - vec(b) - vec(c ) , then which one of the following is correct?

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is