Show that the area of the parallelogram having diagonals `3hati+hatj-2hatk and hati-3hatj+4hatk` is `5sqrt3`

The two adjacent sides of a parallelogram are '2 hati-4 hatj+5 hatk' and 'hati .-2 hatj-3 hatk .' Find the unit vector parallel to its diagonal. Also find its,area.

Find the angle between the vectors hati-2 hatj+3 hatk and 3 hati-2 hatj+hatk

Show that the vectors 2 hati-hatj+hatk, hati-3 hatj-5 hatk and 3 hati-4 hatj-4 hatk form the vertices of a right-angled triangle.

Find the area of the parallelogram whose adjacent sides are determined by the vectors 'veca=hati-hatj+3 hatk' and 'vecb=2 hati-7 hatj+hatk'

Compute the magnitude of the following vectors. veca=hati+hatj+hatk, vecb=2 hati-7 hatj-3 hatk vecc=1/(sqrt3) hati+1/(sqrt3) hatj-1/(sqrt3) hatk

Show that the points with position vectors 2hati+6hatj+3hatk,hati+2hatj+7hatk and 3hati+10hatj-hatk are collinear.

The scalar product of the vector hati+hatj+hatk with a unit vector along the sum of vectors 2 hati+4 hatj-5 hatk and lambda hati+2 hatj+3 hatk is equal to one. Find the value of lambda