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=2veci+vecj-3veck vecB=veci-2vecj+veck and vecC=-veci+vecj-vec4k find vecAxx(vecBxxvecC)

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 .

Find lambda so that the vectors vec a=2 hat i- hat j+ hat k ,\ vec b= hat i+2 hat j-3 hat k\ a n d\ vec c=3 hat i+lambda hat j+5 hat k are coplanar.

i. If vec a , vec b a n d vec c are non-coplanar vectors, prove that vectors 3veca -7vecb -4 vecc ,3 veca -2vecb + vecc and veca + vecb +2 vecc 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)

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.

If vec a= hat i+ hat j+ hat k , vec b= hat i- hat j+ hat k , vec c= hat i+2 hat j- hat k , then find the vaue of | vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec a vec bdot vec a dot vec c dot vec a dot vec c dot vec a dot vec c dot vec a| .

Write the value of lamda so that the vectors vec(a)= 2hat(i) + lamda hat(j) + hat(k) and vec(b)= hat(i) - 2hat(j) + 3hat(k) are perpendicular to each other?

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.