Find the cartesian equation fo the following planes. `vecr.(hati+hatj-hatk)=2`

Find the cartesian equation fo the following planes. vecr.(2hati+3hatj-4hatk)=1

Find the cartesian equation fo the following planes. vecr.[(s-2t)hati+(3-t)hatj+(2s-t)hatk] = 15

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) 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)

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 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 equation of the plane which contains the line of intersection of the planes vecr .(hati+2 hatj+3 hatk)-4 =0 , vecr .(2 hati+hatj-hatk)+5=0 and which is perpendicular to the plane vecr .(5 hati+3 hatj-6 hatk)+8=0