If A,B,C are points (1,0,-1), (0,1,-1) and (-1,0,1)` respectively find the sine of the angle between the lines AB and AC.

In Fig.ABC is a triangle co-ordinates of whose vertex A are (0,-1). D and E respectively are the mid-points of sides AB and AC their co- ordinates are (1,0) and (0,1) respectively.If F is the mid-point of BC find the areas of /_ABC and /_DEF

The sides AB and AD of a parallelogram ABCD are 2x-y+1=0 and x+3y-10=0 respectively and C is the point (-1, -2) . Find the equation of the diagonals AC and BD.

If the points A(3,0,p),B(-1,q,3) and C(-3,3,0) are collinear, then find (1) the ratio in which the points C divides the line segment AB (2) the value of p and q.

If the vertices A, B, C of a triangle ABC are (1," "2," "3)," "(1," "0," "0)," "(0," "1," "2) , respectively, then find /_A B C . [/_A B C is the angle between the vectors vec( B A) and vec (B C) .

If A = [(2,0,1),(-1,1,5)] and B = [(-1,1,0),(0,1,-2)] then find AB'

A straight line through the point A(-2, -3) cuts the line x+3y=9 and x+y+1=0 at B and C respectively. Find the equation of the line if AB.AC = 20 .