[" 13.If "A(1,2,-3)" and "B(-1,-2,1)" are two given points then find the "],[" cosines of "vec AB" ."]

If A(1,2,-3) and B(-1,-2,1) are the two given points in space then find (i) the direction ratios of vec(AB) and (ii) the direction cosines of vec(AB) . Express vec(AB) in terms of hati , hatj and hatk .

If A(-2,1,2) and B(2,-1,6) are two given point, find a unit vector in the direction of vec(AB) .

If A(1,2,4) and B(2,-1,3) are two points (i)Find vec(AB)

If A(8,2,0),B(4,6,-7),C(-3,1,2)and D(-9,-2,4) are four given point then find the angle between vec(AB)and vec(CD) .

If A(1,2,4) and B(2,-1,3) are two points (ii) Find unit vector along vec(AB)

Let A(2,1-3) and B(5,-8,3) be two given points. Find the coordinats of the points of trisection of the line segment AB.

If vec(AB) = (2hati + hatj - 3hatk) and A(1,2,-1) is the given point, find the coordinates of B.

A(3,-1,2),B(2,-3,3) and C(1,-2,1) are three given points . Find the angle between the vectors vec(BA)and vec(BC) .

Let A(2,3,4),B(4,3,2) and C(5,2,-1) be three points .Find the projection of vec(BC) on vec(AB) .

If A (1,2,3), B (-1,2, -3), C (1 , -2, 3) and D (-1, -2, -3) are points in space, then find the angle between the directed lines vec(AB) and vec(CD).