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If p,q,r ar...

Question

If $p, q, r$ are the projections of the line segment $A B$ on the coordinate axes, then $A B$ $=$

A

\sqrt{p q r}

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B

\sqrt{p + q + r}

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C

p^{2} + q^{2} + r^{2}

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D

\sqrt{p^{2} + q^{2} + r^{2}}

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Solution

The correct option is D $\sqrt{p^{2} + q^{2} + r^{2}}$
$p = A B cos α$
$q = A B cos β$
$r = A B cos γ$
$p^{2} + q^{2} + r^{2} = (A B)^{2} [cos α^{2} + cos β^{2} + cos γ^{2}]$
$p^{2} + q^{2} + r^{2} = (A B)^{2} [1]$
$\sqrt{p^{2} + q^{2} + r^{2}} = (A B)$

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Similar questions

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are in AP, then

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B C, C A

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are the sides of a triangle

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whose midpoints are

(p, 0, 0), (0, q, 0), (0, 0, r)

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