#### Question

The distance of the point *P* (*a*, *b*, *c*) from the *x*-axis is

\[\sqrt{b^2 + c^2}\]

\[\sqrt{a^2 + c^2}\]

\[\sqrt{a^2 + b^2}\]

none of these

#### Solution

\[\left( a \right) \sqrt{b^2 + c^2}\]

\[\text{ The projection of the point P } \left( a, b, c \right) \text{ on the x - axis is } \left( a, 0, 0 \right) \text{ as both Y and Z coordinates on any point on the x - axis are equal to zero } . \]

\[ \therefore \text{ Distance of P } \left( a, b, c \right) \text{ from x - axis = Distance of P } \left( a, b, c \right) \text{ from } \left( a, 0, 0 \right)\]

\[ = \sqrt{\left( a - a \right)^2 + \left( b - 0 \right)^2 + \left( c - 0 \right)^2}\]

\[ = \sqrt{b^2 + c^2}\]

Is there an error in this question or solution?

Solution The Distance of the Point P (A, B, C) from the X-axis is ,√ B 2 + C 2√ a 2 + C 2,√ a 2 + B 2,None of These. Concept: Direction Cosines and Direction Ratios of a Line.