Determine whether the pair of straight lines `vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hati-3hatk)+s(hati+2hatj+3hatk)` are parallel.

Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk)+t(2hati+3hatj+4hatk),vecr=(2hatj-3hatk)+s(hati+2hatj+3hatk) are parallel. Find the shortest distance between them.

Determine whether the lines vecr=(hati-hatj)+t(hati-hatj+3hatk) and vecr=(2hati+hatj-hatk)+s(hati+2hatj-hatk) are parallel. Find the shortest distance between them.

Find the distance between the parallel lines vecr=(hati-hatj)+t(2hati-hatj+hatk) and vecr=(2hati+hatj-hatk)+s(2hati-hatj+hatk) .

Find the angle between the following lines. vecr=(4hati-hatj)+t(hati+2hatj-2hatk) vecr =(hati-2hatj+4hatk)+s(-hati-2hatj+2hatk)

Find the non-parametric form of vector equation, and Cartesian equation vector equation, and Cartesian equation of the plane passing through the point (0, 1,-5) and parallel to the straight lines vecr=(hati=2hatj-4hatk)+s(2hati+3hatj+6hatk) and vecr=(hati=3hatj-4hatk)+t(hati+hatj+hatk)

Find the distance between the lines vecr=3hati+2hatj-4hatk+lambda(hati+2hatj+2hatk) and vecr=5hati-2hatk+mu(hati+2hatj+2hatk)

Find the non parametric form of vector equation and the cartesian equation of the plane passing through the point (-1, 2, -3) and parallel to the lines vecr=(2hati-hatj+3hatk)+t(hati+hatj-2hatk) and vecr=(hati-hatj+3hatk)+s(3hati-hatj-2hatk)

Find the angle between the lines vecr=hati-hatj+hatk+lambda(2hati-2hatj+hatk) and vecr=2hati-hatj+2hatk+mu(hati+hatj+2hatk) .