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Question
The distance of the point P (a, b, c) from the x-axis is
Options
\[\sqrt{b^2 + c^2}\]
\[\sqrt{a^2 + c^2}\]
\[\sqrt{a^2 + b^2}\]
none of these
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Solution
\[\left( a \right) \sqrt{b^2 + c^2}\]
\[\text{ The projection of the point P } \left( a, b, c \right) \text{ on the x - axis is } \left( a, 0, 0 \right) \text{ as both Y and Z coordinates on any point on the x - axis are equal to zero } . \]
\[ \therefore \text{ Distance of P } \left( a, b, c \right) \text{ from x - axis = Distance of P } \left( a, b, c \right) \text{ from } \left( a, 0, 0 \right)\]
\[ = \sqrt{\left( a - a \right)^2 + \left( b - 0 \right)^2 + \left( c - 0 \right)^2}\]
\[ = \sqrt{b^2 + c^2}\]
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