The position vectors of the points A,B,C,D are `vec(3i)-vec(2j)-veck, vec(2i)+vec(3j)-vec(4k)-veci+vecj+vec(2k) and vec(4j) +vec(5j)+vec(lamdak)` respectively Find `lamda` if A,B,C,D are coplanar.

The position vectors of the points A,B,C , D are respectively 2 vec i + vec j - vec k, vec i + vec j + vec k, vec i- 2 vec j+ 3 vec k and 3 vec i- vec j + 2 vec k . Evaluate [vec (AB), vec (AC), vec (AD)] .

Examine if vec(i) - 3vec(j) + 2vec(k), 2vec(i) - 4vec(j) - vec(k) and 3vec(i) + 2vec(j) - vec(k) are linearly independent or dependent .

Show that the four points A,B,C and D whose position vectors are (4vec i+5vec j+vec k),(-vec j-vec k),(3vec i+9vec j+4vec k) and (-4vec i+4vec j+4vec k) respectively are coplanar

consider the points A,B,C and D with position vector 7vec i-4vec j+7vec k,vec i-6vec j+10vec k,-vec i-3vec j+4vec k and 5vec i-vec j+vec k respectively then ABCD is

The position vectors of three points are vec i+3vec j-2vec k,3vec i-2vec j+vec k and -2vec i+vec j+3vec k show that the points are the vertices of an equilateral triangle

The position vectors of the points A and B are vec i + 2 vec j + 3 vec k and 2 vec i - vec j - vec k respectively. Find the projection of vec (AB) on the vector vec i + vec j + vec k . Also find the resolved part of vec (AB) in that direction.

The four points whose position vectors are 6vec i-7vec j16vec i-29vec j-4vec k,3vec i-6vec k,2vec i+5vec j+10vec k are

Find the value of the constant lamda so that vectors veca=vec(2i)-vecj+veck, vecb=veci+vec(2j)-vec(3j), and vecc=vec(3i)+vec(lamdaj)+vec(5k) are coplanar.

The position vector of the points A, B and C are respectively vec i + vec j, vec j + vec k and lambda vec k + vec i . If the volume of the tetrahedron OABC is 6, find lambda where O is the origin.

If veca=veci+vec(2j)-veck,vecb=vec(2i)+vecj+vec(3k),vecc=veci-vecj+veck and vecd=vec(3i)vecj+vec(2k) then evaluate (vecaxxvecb)xx(veccxxvecd)