Find the angle between the planes : `vecr*(2hati+2hatj-3hatk)=5 and vecr*(3hati-3hatj+5hatk)=3`

Find the acute angle between the planes vecr.(hati+2hatj-hatk)=3 and vecr.(2hati-hatj+2hatk)=2 .

Find the angle between the planes: vecr.(hati+hatj)=1 and vecr.(hati+hatk)=3 .

Find the vector equation of the plane through the planes : vecr*(hati+hatj+hatk)=6 and vecr*(2hati+3hatj+4hatk)=-5 at the point (1,1,1).

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .

The acute angle between the planes vecr.(2hati-3hatj+hatk)=1 and vecr.(hati-2hatj)=2 is………………. .

Find the angle between the following pair of lines : vecr=hati+hatj-hatk+lambda(hati-3hatj+2hatk), vecr=2hati-hatj+hatk+mu(3hati+hatj-2hatk)

Find the angle between the line : vecr=(hati-hatj+hatk)+lambda(2hati-hatj+3hatk) and the plane vecr*(2hati+hatj-hatk)=4 . Also find whether the line is parallel to the plane or not.

Find the angle between the line vecr=(hati+2hatj-hatk)+lambda(hati-hatj+hatk) and the plane vecr.(2hati-hatj+hatk)=4 .

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

The square of the shortest distance between the lines : vecr=s(hati-hatj-hatk) and vecr=3hatj+t(hati-hatk) is :