List of top Mathematics Questions on introduction to three dimensional geometry asked in KEAM

The projections of a line segment on the coordinate axes are \(5,6,8\). Then the length of the line segment is

Let \( \alpha, \beta \) and \( \gamma \) be the angles made by a straight line with the x-axis, y-axis and z-axis respectively. If \( \cos\alpha + \cos\beta + \cos\gamma = \frac{5}{3} \), then the value of \( \cos\alpha \cos\beta + \cos\beta \cos\gamma + \cos\gamma \cos\alpha \) is equal to

If the equation of the sphere through the circle $x^2 + y^2 + z^2 = 5$, $2x + 3y + 4z = 5$ and through the origin is $x^2 + y^2 + z^2 - 2x - 3y - 4z + C = 0$, then the value of $C$ is