`P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(,-2,-1),` then find the projection length of ` vec P Qon vec R Sdot`

A tetrahedron has vertices P(1,2,1),Q(2,1,3),R(-1,1,2) and O(0,0,0) . The angle beween the faces OPQ and PQR is :

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

If [{:(0,p,3),(2,q^2 , -1),(r, 1,0):}] is skew-symmetric , find the values of p , q and r

If [(0,p,3),(2,q^(2),-1),(r,1,0)] is skew- symmetric, find the values of p,q, and r.

Consider the triangle ABC with vertices A(1,2,3) , B(-1, 0, 4) and C(0, 1, 2) (a) Find vec (AB) and vec (AC) Find angle A . (c) Find the area of triangle ABC.

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) Find the area of trianglePQR .

Let for A=[(1,0,0),(2,1,0),(3,2,1)] , there be three row matrices R_(1), R_(2) and R_(3) , satifying the relations, R_(1)A=[(1,0,0)], R_(2)A=[(2,3,0)] and R_(3)A=[(2,3,1)] . If B is square matrix of order 3 with rows R_(1), R_(2) and R_(3) in order, then The value of det. (2A^(100) B^(3)-A^(99) B^(4)) is

The vertices of trianglePQR are P(0,-4),Q(3,1) and R(-8,1) Find the coordinates of N, the mid-point of QR.

On the xy plane where O is the origin, given points, A(1,0), B(0,1) and C(1,1). Let P,Q, and R be moving points on the line OA, OB, OC respectively such that vec(OP)=45t(vec(OA)), vec(OQ)=60t(vec(OB)), vec(OR)=(1-t)(vec(OC)) with t gt 0 . If the three points P,Q and R are collinear then the value of t is equal to