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.

Find the volume of the parallelopiped whose edges are represented by veca=vec(2i)-vec(3j)+vec4k, vecb=veci+vec(2j)-veck and vecc=vec(3i)-vecj+vec(2k)

if the vectors vec a=vec i+vec j+vec k, , b=vec i-vec j+2vec k and vec c=xvec i+(x-2)vec j-vec k are coplanar then x is

Find the angle between the vectors : vec(a)=3vec(i)-2vec(j)+vec(k) and vec(b)=vec(i)-2vec(j)-3vec(k)

Find the angle between the following vectors: (i)vec a=vec i+2vec j+2vec kvec b=vec i-2vec j+2vec k

If a=vec i+4vec j,vec b=2vec i-3vec j and vec c=5vec i+9vec j then vec c=

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

The number of distinct real values of lambda for which the vectors -lambda ^ (2) vec i + vec j + vec k, vec i-lambda ^ (2) vec j + vec k, vec i + vec j-lambda ^ ( 2) vec k are coplanar is

Find the unit vector in the direction of the vector vec a + vec b if vec a =vec i +2 vec j + 3 vec k and vec b = 2 vec i + 3 vec j + 5 vec k .

The sine of the angle between the vectors vec i+3vec j+2vec k and 2vec i-4vec j+vec k is

The value of lambda for two perpendicular vectors vec(A)=2vec(i)+lambdavec(j)+vec(k) and vec(B)=4vec(i)-2vec(j)-2vec(k) is :-