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

A straight line passing through (6,1,3) meets the line \( \frac{x-1}{2} = \frac{y}{1} = \frac{z-2}{3} \) at Q. If the lines are perpendicular to each other, then the coordinates of Q are:

If the equation of the sphere through the circle \( x^2 + y^2 + z^2 = 9; \; 2x + 3y + 4z = 5 \) and through the point \( (1,2,3) \) is \( 3(x^2 + y^2 + z^2) - 2x - 3y - 4z = C \), then the value of \( C \) is

If a straight line makes the angles \(60^\circ,45^\circ,\alpha\) with x, y and z axes respectively, then \( \sin^2\alpha \) is

If a straight line makes angles \( \alpha, \beta, \gamma \) with the coordinate axes, then evaluate \[ 1 - \frac{\tan^2\alpha}{1+\tan^2\alpha} + \frac{1}{\sec^2\beta} - 2\sin^2\gamma \]