List of top Mathematics Questions on Three Dimensional Geometry asked in BITSAT

Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines PN and PQ, then \( \cos \alpha \) is equal to

The magnitude of projection of line joining (3, 4, 5) and (4, 6, 3) on the line joining (−1, 2, 4) and (1, 0, 5) is