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

If PxxQ={(2,-1),(3,0),(2,1),(3,1),(2,0),(3,-1)} , find P and Q.

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

A(p,1,-1), B (2p,0,2) and C(2+2p,p,p) are three points . Find the value of p so that the vectors vec(AB) and vec(BC) are perpendicular to each other .

If P-=(1,0), Q-=(-1, 0), R-=(2,0) are three given points, then the locus of the point S satisfying the condition SQ^2+SR^2=2SP^2 is

If the points P (0,3,2), Q(1,2,-2) and R (4,-1,t) are collinear, find the value of t.

If .^(n+r+1)P_(2)=72and.^(n-r)P_(2)=12 then find the values of n and r.

IF p^3-q(3p-1)+q^2=0 , find the relation between the roots of the equation x^2+px+q=0 .

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. (B) is

Let P=[(1,2,1),(0,1,-1),(3,1,1)] . If the product PQ has inverse R=[(-1,0,1),(1,1,3),(2,0,2)] then Q^(-1) equals

Suppose that vec(p), vec(q) and vec(r) are three non-coplanar vectors in R. Let the components of a vector vec(s) along vec(p), vec(q) and vec(r) be 4, 3 and 5 respectively. If the components of this vector vec(s) " along" (-vec(p) + vec(q) + vec(r)), (vec(p) - vec(q) + vec(r)) and (-vec(p) - vec(q) + vec(r)) are x,y and z respectively, then the value of 2x + y + z is