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.

Vectors vec(3i)-vec(2i)+veck and vec(2i)+vec(6j)+vec(mk) will be perpendicular to each other if

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.

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).(veccxxvecd)

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)

If veca=-vec(2i)-vec(2j)+vec(4k),vecb=-vec(2i)+vec(4j)-vec(2k) and vecc=vec(4i)-vec(2j)-vec(2k) Calculate the value of [veca vecb vecc\] and interpret the result.

Find the volume of the parallelopiped whose thre coterminus edges asre represented by vec(2i)+vec(3j)+veck, veci-vecj+veck, vec(2i)+vecj-veck .

The position vectors of points A, B, C and D are : vec(A) = 3hat(i) + 4hat(j) + 5hat(k), vec(B) = 4hat(i) + 5hat(j) + 6hat(k) vec(C ) = 7hat(i) + 9hat(j) + 3hat(k) and vec(D) = 4hat(i) + 6hat(j) Then the displacement vectors vec(AB) and vec(CD) are :

Examine the following vector for linear independence: (1) vec i+vec j+vec k ,2vec i+3vec j-veck,-vec i-2vecj+2vec k (2) 3veci+vec j-vec k, 2vec i-vec j+7 vec k, 7 veci-vec j+13vec k

If vec a= i- j and vec b=- j+2k ,find (vec a-2 vec b)dot( vec a+ vec b)

If vec a=2 vec i+3 vec j- vec k , vec b=- vec i+2 vec j-4 vec k a n d vec c= vec i+ vec j+ vec k , then find thevalue of ( vec axx vec b) dot ( vec axx vec c)dot