The diagonals of a parallelogram are represented by ` vec R_1 = 3 hat i + 2 hat j - 7 hat k` and `vec R_2 = 5 hat i + 6 hat j - 3 hat k`. Find the area of the parallelogram.

The diagonals if a parallele-gram are representde by vec d_(1) =2 hat I + 3 hat j -5 hat k and vec d_(2) =6 hat I + 5 hat j -3 hat k . Find the area of the parallelogram.

Angle between diagonals of a parallelogram whose side are represented by vec a=2hat i+hat j+hat k and vec b=hat i-hat j-hat k

The adjacent sides of a parallelogram are represented by the vectors vec a=hat i+hat j-hat k and vec b=-2hat i+hat j+2hat k Find unit vectors parallel to the diagonals of the parallelogram.

If vec A =4 hat I + 6 hat j -3 hat k and vec B =- 2 hat I -5 hat j + 7 hat k , find the angle between vec A and vec B .

If vec A = hat i + 3 hat j + 2 hat K and vec B = 3 hat i + hat j + 2 hat k , then find the vector product vec A xx vec B .

Find the area of a parallelogram whose adjacent sides are given by the vectors vec a=3hat i+hat j+4hat k and vec b=hat i-hat j+hat k

Determine the area of the parallelogram whose adjacent sides are formed by the vectors vec A = hat i -3 hat j + hat k and vec B = hat i + hat j + hat k .

Find the area of the parallelogram whose adjacent sides are determined by the vectors vec a=hat i-hat j+3hat k and vec b=2hat i-7hat j+hat k

Let ABCD be the parallelogram whose sides AB and AD are represented by the vectors 2 hat i +4 hat j-5 hat k and hat i+2 hat j+3 hat k.Then if vec a is a unit vector parallel to AC then = (a) 1/3(3 hat i-6 hat j-2 hat k) (b) 1/3(3 hat i +6 hat j+2 hat k) (c) 1/7(3 hat i +6 hat j+2 hat k) (d) 1/7(3 hat i +6 hat j-2 hat k)

If vec(a) = 5 hat(i) - hat(j) - 3 hat(k) and vec(b) = hat(i) + 3 hat(j) - 5 hat(k) , find the angle between vec(a) and vec(b) .