Find the value of `(veci-2j+veck)xx[(2veci+vecj+veck)xx(veci+2vecj-veck)]`

If is given that vecx= (vecbxxvecc)/([veca,vecb,vecc]), vecy=(veccxxveca)/[(veca,vecb,vecc)], vecz=(vecaxxvecb)/[(veca,vecb,vecc)] where veca,vecb,vecc are non coplanar vectors. Find the value of vecx.(veca+vecb)+vecy.(vecc+vecb)+vecz(vecc+veca)

Examine the following vectors for linear independence : i. veci+vecj+veck, 2veci+vecj-veck, -veci -2vecj+2veck ii. 3veci+vecj-veck, 2veci-vecj+7veck, 7veci-vecj+13veck

Find the cosine of the angle between the planes vecr.(2veci-3vecj-6veck)=7 and vecr.(6veci+2vecj-9veck)=5

Find the angle between planes vecr.(veci+vecj)=1 and vecr.(veci+veck)=3 .

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

If veca vecb are non zero and non collinear vectors, then [(veca, vecb, veci)]hati+[(veca, vecb, vecj)]hatj+[(veca, vecb, veck)]hatk is equal to

Prove that the four points 4veci+5veci+veck, -(vecj+veck),3veci+9vecj+4veck and 4(-veci+vecj+veck) are coplanar

Examine whether the vectors veca=2veci+3vecj+2veck, vecb=veci-vecj+2veck and vecc=3veci+2vecj-4veck form a left handed or a righat handed system.

If a vector vecr of magnitude 3sqrt6 is directed along the bisector of the angle between the vectors veca =7veci-4vecj -4veck and vecb = -2veci- vecj+ 2veck , then vecr is equal to

The norm of vector vecV=3veci-sqrt2vecj is