Find the value of `a` so that the volume of the parallelepiped formed by vectors ` hat i+a hat j+k , hat j+a hat ka n da hat i+ hat k` becomes minimum.

The value of a so that the volume of parallelepiped formed by hat i+ahat j+hat k,hat j+ahat k and ahat i+hat k is minimum is -3 b.3 c.1/sqrt(3)d.sqrt(3)

If the volume of parallelopiped formed by the vectors hat i+lambdahat j+hat k,hat j+lambdahat k and lambdahat i+hat k is minimum then lambda is equal to

Find the area of the parallelogram determined by the vectors: hat i-3hat j+hat k and hat i+hat j+hat k

The angle between the vectors (hat i + hat j + hat k) and ( hat i - hat j -hat k) is

Write the value of [ hat i- hat j\ hat j- hat k\ hat k- hat i]

The value of p so that vectors 2hat i-hat j+hat k , hat i+2hat j-3hat k and 3hat i+phat j+5hat k are coplanar is

If the vectors 3 hat i +3 hat j +9 hat k and hat i +a hat j +3 hat k are parallel, then a =

Find the volume of the parallelepiped whose coterminous edges are represented by the vectors: vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j+2 hat k vec a=2 hat i+3 hat j+4 hat k , vec b= hat i+2 hat j- hat k , vec c=3 hat i- hat j-2 hat k vec a=11 hat i , vec b=2 hat j- hat k , vec c=13 hat k 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

Find the area of the parallelogram determined by the vectors: 2hat i and 3hat j2hat i+hat j+3hat k and hat i-hat j3hat i+hat j-2hat k and hat i-3hat j+4hat khat i-3hat j+hat k and hat i+hat j+hat k

Find the volume of the parallelepiped whose coterminous edges are represented by the vector: vec a=2hat i+3hat j+4hat k,vec b=hat i+hat i+2hat j-hat k,vec c=3hat i-hat j+2hat k