Find `lambda` if the vectors `vec a= vec i+3 vec j+ vec k` ,`vec b= 2 vec i- vec j- vec k` and `vec c= lambda vec i+7 vec j+ 3 vec k` are coplanar

Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec k " and " -vec j + 2 vec k are coplanar.

Show that the vector veci -2 vec j +3 vec k , -2 vec i + 3 vecj -4 vec k " and " -vec j + 2 vec k are coplanar.

Show that the vectors vec a, vec b and vec c are coplanar if vec a + vec b, vec b + vec c, vec c+ vec a are coplanar.

If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

Consider the vectors vec a = hat i + 3 hat j + hat k , vec b = 2 hat i - hat j - hat k and vec c = lambda hat i + 7 hat j + 3 hat k (i) Find [ vec a, vec b, vec c] (ii) Find the value of lambda , if the vectors vec a, vec b and vec c are coplanar.

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

Find a unit vector vec c if vec -i+vec j-vec k bisects the angle between vec c and 3 vec i+4vec j .

Find the angle between the line vec r=( vec i+2 vec j- vec k)+lambda( vec i- vec j+ vec k) and the normal to the plane vec rdot((2 vec i- vec j+ vec k))=4.

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 vec cdot vec a vec cdot vec a vec cdot vec a| .

Let vec a= vec i- vec k , vec b=x vec i+ vec j+(1-x) vec k and vec c=y vec i+x vec j+(1+x-y) vec k . Then [ vec a vec b vec c] depends on (A) only x (B) only y (C) Neither x nor y (D) both x and y