The ratio in which the plane `vecr.(veci-2 vecj+3veck)=17` divides the line joining the points `-2veci+4vecj+7veckandvec3i-5vecj+8veck` is

The ratio in which the plane vecr ( veci -2 hatj + 3 hatk) = 17 divides the line joining the points - 2vec i + 4 vecj + 7 veck and 3 veci - 5 vecj + 8 veck is

Find the vector equation of the line joining the points 2veci+4j+3veck and -4veci+3vecj-veck .

Find the angle between the vectors 3veci-4vecj+veck and veci-3vecj+4veck .

Find the angle between the vectors veci+2vecj+3veck and 3veci-vecj+2veck

The angle between the two vectors- 2veci+3vecj+veck and veci+3vecj-4veck is.

Find the equation of the plane through the origin and the points 4vecj and 2veci+veck. Find also the point in which this plane is cut by the line joining points veci-2vecj+veck and 3veck-2vecj .

Find the equation of the plane through the origin and the points 4vecj and 2veci+veck. Find also the point in which this plane is cut by the line joining points veci-2vecj+veck and 3veck-2vecj .

Find the vector equation of the line through the points 2veci+vecj-3veck and parallel to vector veci+2vecj+veck

The shortest distance between the lines vecr = (2 veci -vecj - veck) + lamda ( 2 veci + vecj + 2 veck) and vecr = (veci + 2 vecj + veck) + mu ( veci - vecj + veck) is

Find the shortest distance between the following pair of parallel lines whose equation are: vecr = veci + 2 vecj + 3veck + lamda (veci - vecj + veck) and vecr = 2 veci - vecj - veck + mu (-veci + vecj - veck) is