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

If the foot of the perpendicular drawn from the point \( (0,2,1) \) on a line passing through \( (a,5,1) \) is \( \left(\frac{5}{3}, \frac{7}{3}, \frac{15}{3}\right) \), then \( a \) is equal to ___.

If \(\alpha,\beta,\gamma\) are direction angles, then \(\sin^2\alpha+\sin^2\beta+\sin^2\gamma\) is

If \(A(-1,3,2), B(2,3,5), C(3,5,-2)\) are vertices of a triangle ABC, then angles of Triangle ABC are :

A perpendicular is drawn from the point \( P(2,4,-1) \) to the line \( \frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9} \). The equation of the perpendicular from \( P \) to the given line is

If a line in the space makes angle \( \alpha, \beta, \gamma \) with the coordinate axes, then \( \cos 2\alpha + \cos 2\beta + \cos 2\gamma + \sin^{2}\alpha + \sin^{2}\beta + \sin^{2}\gamma \) equals