Given three points are `A(-3,-2,0),B(3,-3,1)a n dC(5,0,2)dot` Then find a vector having the same direction as that of ` vec A B` and magnitude equal to `| vec A C|dot`

Find a unit vector in the direction of vec(AB) , where A(1, 2, 3) and B( 2, 3, 5) are the given points.

A vector vec(A) When added to the vector vec(B)=3hat(i)+4hat(j) yields a resultant vector that is in the positive y-direction and has a magnitude equal to that of vec(B) . Find the magnitude of vec(A) .

A vector vec A when added to the vector vec B = 3. 0 hat i+ 4 hat j yields a resultant vector that is in the positive y-direction and has a magnintude equal to that of vec B . Find the magnitude of vec A .

If A( vec a),B( vec b)a n dC( vec c) are three non-collinear points and origin does not lie in the plane of the points A ,Ba n dC , then point P( vec p) in the plane of the A B C such that vector vec O P is _|_ to planeof A B C , show that vec O P=([ vec a vec b vec c]( vec axx vec b+ vec bxx vec c+ vec cxx vec a))/(4^2),w h e r e is the area of the A B Cdot

If the three successive vertices of a parallelogram have the position vectors as, A(–3, –2, 0), B(3, –3, 1) and C(5, 0, 2). Then find The angle between vec(AC) and vec(BD) .

If vec a\ a n d\ vec b are unit vectors then write the value of | vec axx vec b|^2+( vec adot vec b)^2dot

If the position vectors of the points A(3,4),B(5,-6) and (4,-1) are vec a,vec b,vec c respectively compute vec a+2vec b-3vec c

If vec a,vec b,vec c and vec d are the position vectors of the points A,B,C and D respectively in three dimensionalspace no three of A,B,C,D are collinear and satisfy the relation 3vec a-2vec b+vec c-2vec d=0, then

Given: vec a+vec b+vec c=0. Out off three vectors vec a,vec b and vec c two are equal in magnitude.The magnitude of third vector is sqrt(2) xx that of either of the two having equal magnitude.The angle between vectors is

If vec c=3vec a+4vec b and 2vec c=vec a-3vec b show that (i)vec c and vec a have the same direction and |vec c|>|vec a|(ii)vec b and vec c have opposite direction and |vec c|>|vec b|