The vector `vec v= vec AB` has components 3,-4 and 5 and the point A has the coordinates(2,-3,1). Find the point B.

If A is the point (1,2) and the vector vec AB has components 2 and 6, find the point B.

Find the coordinates of the final point of vector vec v whose components are 2,3,-4 and whose initial point is (3,-6,2). Also find |quad vec v| .

A vector vec r has length 21 and its direction ratios are proportional to 2,-3,6. Find the direction cosines and components of vec r , is given that vec r Makes an acute angle with x-axis

In each of the following problems, components of vec AB along X-axis and Y-axis are respectively a underset 1 and a underset 2 . Find the point B when: a underset 1 = 2, a underset 2 = 3, A(2,-3) .

Find the components o fteh vector vec AB where A and B are the points(2,0,3) and (-1,2,-3) respectively. Also , find the length of this vector.

A,B,C and D are four points with position vectors vec a , vec b , vec c and vec d respectively such that 5 vec a - 2 vec b + 6 vec c- 9 vec d= vec 0 . Show that the point A,B,C,D are coplanar and find find the P.V. of the point in which the lines AC and BD intersects.

If the position vector of a point A is vec a + 2 vec b and vec a divides AB in the ratio 2:3 , then the position vector of B, is

The points A(4, 5, 10), B(2, 3, 4) and C(1, 2, -1) are three vertices of a parallelogram ABCD. Find the vector equations of side AB and BC and also find the coordinates of point D .

Statement 1: if three points P ,Qa n dR have position vectors vec a , vec b ,a n d vec c , respectively, and 2 vec a+3 vec b-5 vec c=0, then the points P ,Q ,a n dR must be collinear. Statement 2: If for three points A ,B ,a n dC , vec A B=lambda vec A C , then points A ,B ,a n dC must be collinear.

In each of the following problems, components of vec AB along X-axis and Y-axis are respectively a_1 and a_2 . Find the point B when: a _1= -5, a_2= 4, A(7,8) .