`vec j*vec k=`

The values of a for which the points A,B,C with position vectors 2vec i-vec j+vec k+vec i-3vec j-5vec k and avec i-3vec j+vec k,vec i-3vec j-5vec k and avec i-3vec j+vec k are the vertices of a right angled triangle with /_C=(pi)/(2) are

If vec r = 3vec i + 2vec j-5vec kvec a = 2vec i-vec j + vec k, vec b = vec i + 3vec j-2vec k and vec c = -2vec i + vec j-3vec k such that vec r = lambdavec a + muvec b + deltavec c then mu, (lambda) / (2), delta are in? (A) AP (B) GP (C) HP (D) AGP

A=4vec i+5vec j+6vec k,B=5vec i+6vec j+4vec k and C=6vec i+4vec j+5vec k are the vertices of

One of the diagonals of a parallelopiped is 4vec j-8vec k, If the 2 diagonals of its face are 6vec i+6vec k and 4vec j+2vec k then volume is:

(3vec i+4vec j-5vec k)*vec i=

Prove that vector vec i-2vec j+5vec k and -2vec i+4vec j+2vec k are mutually Is perpendicular|

Let vec r=vec a+lambdavec l and vec r=vec b+muvec m be two lines in space where vec a=5vec i+vec j+2vec k,b=-vec i+7vec j+8vec k,vec l=-4vec i+vec j-vec k and vec m=2vec i-5vec j-7vec k then the p.v. of a point which lies on both of these lines,is (A) hat i+2hat j+hat k(B)2hat i+hat j+hat k(C)hat i+hat j+2hat k(D) non existence as the lines are skew

If ABCD is a quadrilateral such that vec AB=vec i+2vec AD=vec j+2vec k and vec AC=2(vec i+2vec j)+3(vec j+2vec k) then area is

The ratio in which the line segment joining the points with P.V'Svec i+2vec j+3vec k,-3vec i+6vec j-8vec k is divided by xy-plane is :

If a vector vec r of magnitude 3sqrt(6) is directed along the bisector of the angle between the vectors vec a=7vec i-4vec j-4vec k and vec b=-2vec i-vec j+2vec k, then vec r is equal to