Prove that the lines x=2 `(y-1)/(3) = (z-2)/(1)` and `x = (y-1)/(1) = (z+1)/(3)` are skew lines.

Prove that the lines (x+1)/(3)=(y+3)/(5)=(z+5)/(7) and (x-2)/(1)=(y-4)/(4)=(z-6)/(7) are coplanar. Also, find the plane containing these two lines

Show that the lines (x+3)/(-3)=(y-1)/(1)=(z-5)/(5) and (x+1)/(-1)=(y-2)/(2)=(z-5)/(5) are coplanar.

The angle between the lines (x+1)/(2) + (y+3)/(2) = (z-4)/(-1) and (x-4)/(1) = (y+4)/(2) = (z+1)/(2) is........

The lines (x-1)/(3) = (y-1)/(-1) = (z+1)/0 and (x-4)/(2) = (y+0)/(0) = (z+1)/(3) are ......

The plane passes through the point (1,-1,-1) and its normal is perpendicular to both the lines (x-1)/(1) = (y+2)/(-2) = (z-4)/(3) and (x-2)/(2) + (y+1)/(-1) = (z+7)/(-1) . The distance of the point (1,3,-7) from thise plane is ..........

If the lines (2x-5)/(k) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) = (z)/(3) are perpendicular to each other, then value of k is....................

The shortest distance the lines (x-3)/(3) = (y-8)/(-1) = (z-3)/(1) and (x+3)/(-3) = (y + 7)/(2) = (z-6)/(4) is..........

The plane containing the two lines (x-3)/(1) = (y-2)/(4) = (z-1)/(5) and (x-2)/(1) = (y+3)/(-4) = (z+1)/(5) is 11x+my + nz = 28 where .............

Find the magnitude of the shortest distance between the lines (x)/(2)=(y)/(-3)=(z)/(1) and (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) .