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.

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) .

Show that the four points S(0,-1,0), B(2,1,01), C(1,1,1) and D(3,3,0) are coplanar. Find the equation of the plane containing them.

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the line L is

If A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2) then the centre of the circle for which the lines AB,BC, CA are tangents is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. Q. The perpendicular distance of D from the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C. The equation of the plane ABC is

Given four points A(2, 1, 0), B(1, 0, 1), C(3, 0, 1) and D(0, 0, 2) . Point D lies on a line L orthogonal to the plane determined by the points A, B and C.

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.

If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) , respectively, then find angleABC .

Let there are three points A (0, 4/3), B(–1, 0) and C(1, 0) in x – y plane. The distance from a variable point P to the line BC is the geometic mean of the distances from this point to lines AB and AC then locus of P can be