Show that the straight lines `x+1=2y=-12zandx=y+2=6z-6` are skew and hence find the shortest distance between them.

Show that the straight line x-2y+3=0 and 6x+3y+8=0 are perpendicular .

Show that the lines vecr=(6hati+hatj+2hatk)+s(hati+2hatj-3hatk) and vecr=(3hati+2hatj-2hatk)+t(2hati+4hatj-5hatk) are skew lines and hence find the shortest distance between them.

Show that the lines vecr=(3hati+5hatj+7hatk)+t(hati-2hatj+hatk) vecr=(hati+hatj+hatk)+s(7hati+6hatj+7hatk) are skew lines and find the shortest distance between them.

Show that the lines (x-3)/(1)=(y-5)/(-2)=(z-7)/(1) and (x-1)/(7)=(y-1)/(6)=(z-1)/(7) are skew lines and find the shortest distance between them.

For the straight lines 4x+3y-6=0 and 5x+12 y+9=0, find the equation of the bisector of the obtuse angle between them, bisector of the acute angle between them, and bisector of the angle which contains (1, 2)

Show that the equation 4x^(2)+4xy+y^(2)-6x-3y-4=0 represents a pair of parallel lines. Find the distance between them.