If the vectors `2 hat i-3 hat j , hat i+ hat j- hat ka n d3 hat i- hat k` form three concurrent edges of a parallelepiped, then find the volume of the parallelepiped.

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 altitude of a parallelepiped whose three coterminous edtges are vectors vec A= hat i+ hat j+ hat k , vec B=2 hat i+4 hat j- hat ka n d vec C= hat i+ hat j+3 hat kw i t h vec Aa n d vec B as the sides of the base of the parallepiped.

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

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

If vec a= hat i+ hat j+ hat k , vec b=2 hat i- hat j+3 hat k a n d vec c= hat i-2 hat j+ hat k find a unit vector parallel to 2 vec a- vec b+3 vec cdot

Find the angle between the vectors hat i-2hat j+3hat k and 3hat i-2hat j+hat k

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :

If hat i+ hat j+ hat k , 2 hat i+5 hat j , 3 hat i+2 hat j-3 hat k a n d hat i-6 hat j- hat k espectively are the position vectors of points A , B , C a n d D then find the angle between the straight lines A B a n d C Ddot Deduce that A B a n d C D are collinear.

If vectors hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3hat(j) - a hat(k) are equal vectors, then the value of a is :