Show that the vectors `cos(A-P)veci+cos(A-Q)vecj+cos(A-R)veck,cos(B-P)veci+cos(B-Q)vecj+cos(B-R)veck and cos(C-P)vecicos(C-Q)vecj+cos(C-R)veck` are coplanar.

Prove that |{:(cos(A-P),cos(A-Q),cos(A-R)),(cos(B-P),cos(B-Q),cos(B-R)),(cos(C-P),cos(C-Q),cos(C-R)):}| =0.

For all values of A ,B ,Ca n dP ,Q ,R show that |"cos"(A-P)"cos"(A-Q)"cos"(A-R)"cos"(B-P)"cos"(B-Q)"cos"(B-R)"cos"(C-P)"cos"(C-Q)"cos"(C-R)|=0

Prove that for any nonzero scalar a the vectors aveci+2avecj-3aveck, (2a+1)veci+(2a+3)vecj+(a+1)veck and (3a+5)veci+(a+5)vecj+(a+2)veck are non coplanar

Prove that: cos(A+B+C)+cos(A-B+C)+cos(A+B-C)+cos(-A+B+C)=4cos A\ cos B\ cos C

Show that: sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0

Show that : cos A+ cosB + cosC+ cos(A+B+C) = 4cos""(B+C)/(2)cos""(C+A)/(2)cos""(A+B)/(2) .

|(1,cos(A-B), cos(A-C)),(cos(B-A), 1, cos(B-C)),(cos(C-A), cos(C-B), 1)| (A) 0 (B) 1 (C) cosAcosBcosC (D) none of these

Find the equation of the plane passing through three given points A(-2veci+6vecj-6veck),B(-3veci+10vecj-9veck) and C(-5veci+vec(6k))

A unit vector coplanar with veci + vecj + 2veck and veci + 2 vecj + veck and perpendicular to veci + vecj + veck is _______

Let points P,Q, and R hasve positon vectors vecr_1=3veci-2vecj-veck, vecr_2=veci+3vecj+4verck and vecr_3=2veci+vecj-2veck relative to an origin O. Find the distance of P from the plane OQR.