Find the value of `lambda` if the volume of a tetrashedron whose vertices are with position vectors ` hat i-6 hat j+10 hat k ,- hat i-3 hat j+3 hat k ,5 hat i- hat j+lambda hat ka n d7 hat i-4 hat j+7 hat k` is 11 cubic unit.

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

Find the value of mu if the points with position vectors hat i - hat j + 3 hat k and 3 hat i + 4 hat j+ mu hat k are equidistant form the plane hat r .(5 hat i + 2 hat j - 7 hat k )+ 8 =0

If the four points with positing vectors,-2hat i+hat j+hat k,hat i+hat j+hat k,hat j-hat k and lambdahat j+hat k are coplanar,then lambda is equal to

Find the value of lambda for which the four points with position vectors -hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and 4hat i+4hat j+4hat k are coplanar.

Find the value of lambda for which the four points with position vectors hat j-hat k,4hat i+5hat j+lambdahat k,3hat i+9hat j+4hat k and -4hat i+4hat j+4hat k are coplanar.

Find the projection of vector hat i+3hat j+7hat k on the vector 7hat i-hat j+8hat k

Find a set of vectors reciprocal to the set -hat i+hat j+hat k,hat i-hat j+hat k,hat i+hat j+hat k

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

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

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.