Find the angle between the planes whose vector equations are
`vecr.(2hati+2hatj-3hatk)=5` and `vecr.(3hati-3hatj+5hatk)=3`

Find the shortest distance between the lines whose vector equations are vecr=(hati+2 hatj+3 hatk)+lambda(hati-3 hatj+2 hatk) and vecr=(4 hati+5 hatj+6 hatk)+mu(2 hati+3 hatj+hatk)

Find the equation of the plane passing through the line of intersection of the planes vecr .(hati+hatj+hatk)=1 and vecr.(2 hati+3 hatj-hatk)+4=0 and parallel to x -axis.

Find |vecaxxvecb| ,If veca=2hati-hatj+3hatk and vecb=hati+2hatj-hatk

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

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