Find the value of `(3hati-hatj+5hatk)-(hati-5hatj+3hatk)`

Find the shortest distance between the lines vecr =(2hati-hatj-hatk)+lambda(3hati-5hatj+2hatk) and vecr =(hati+hatj+hatk)+mu(hati-hatj+hatk)

Find the shortest distance between the lines vecr = hati+hatj+lambda(2hati-hatj+hatk) and vecr = (2 hati+hatj-hatk) + mu (3hati-5hatj + 2hatk)

Find the value of p, if the vectors hati - 2hatj + hatk , 2hati - 5hatj + phatk and 5hati - 9hatj + 4hatk are coplanar .

Find the angle between the following pairs of lines. vecr = 3hati+hatj-hatk+lambda(hati-hatj-hatk) vecr = 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the angle between the following pairs of lines. (i) hatr = 2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and vecr = 7 hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr = 3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr= 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the angle between the following pairs of lines. (i) hatr = 2hati-5hatj+hatk+lambda(3hati+2hatj+6hatk) and vecr = 7 hati-6hatk+mu(hati+2hatj+2hatk) (ii) vecr = 3hati+hatj-2hatk+lambda(hati-hatj-2hatk) and vecr= 2hati-hatj-56hatk+mu(3hati-5hatj-4hatk)

Find the volume of a cuboid whose edges are given by -3hati+7hatj+5hatk, -5hati+7hatj-3hatk and -7hati-5hatj-3hatk

Using scalar triple product, find the volume of the parallelopiped whose sides are given by the vectors 7hati-5hatj-3hatk , hati+2hatj-hatk and -3hati+7hatj+5hatk .

Examine whether the vectors hati+3hatj+hatk,2hati-hatj-hatk and 7hatj+5hatk are coplanar.