If the two diagonals of one its faces are `6 hat i+6 hat ka n d4 hat j+2 hat k` and of the edges not containing the given diagonals is `c=4 hat j-8 hat k ,` then the volume of a parallelepiped is `60` b. `80` c. `100` d. `120`

If the vectors 2hat i-3hat j,hat i+hat j-widehat k and 3hat i-hat k form three concurrent edges of a parallelepiped,then find the volume of the parallelepiped.

Find the area of the parallelogram whose diagonals are 2hat i+hat j and hat i+hat j+hat k

Find the area of the parallelogram whose diagonals are: 2hat i+hat k and hat i+hat j+hat k

If in parallelogram ABCD, diagonal vectors are vec A C=2 hat i+3 hat j+4 hat k and vec B D=-6 hat i+7 hat j-2 hat k , then find the adjacent side vectors vec A B and vec A D

vec A B=3 hat i- hat j+ hat ka n d vec C D=-3 hat i+2 hat j+4 hat k are two vectors. The position vectors of the points Aa n dC are =6 hat i+7 hat j+4 hat ka n d=-9 hat j+2 hat k respectively. Find the position vector of a point P on the line A B and a point Q on the line C D such that vec P Q is perpendicular to vec A Ba n d vec C B both.

If vec a= hat i+ hat j- hat k ,\ vec b=- hat i+2 hat j+2 hat k\ a n d\ vec c=- hat i+2 hat j- hat k , then a unit vector normal to the vectors a+b\ a n d\ b-c is hat i b. hat j c. hat k d. none of these

If the volume of a parallelepiped whose adjacent edges are vec a=2hat i+3hat j+4hat k,vec b=hat i+alphahat j+2hat k,vec c=hat i+2hat j+alphahat k is 15, then find the value of alpha if (alpha>0)

vec a=4hat i-hat j+hat k+hat k,vec b=2hat i+hat j+7hat k,vec c=-3hat i-4hat j+2hat k and vec d=hat i+hat j+hat k then find the value of 3vec a+2vec b-4vec c-vec d

Find the area of the parallelogram whose diagonals are: 3hat i+4hat j and hat i+hat j+hat k

What is the area of the parallelogram having diagonals 3hat(i) + hat(j) - 2 hat(k) and hat(i) - 3 hat(j) + 4 hat(k) ?