If the projections of a line segment on the x, y and z axes in $3$ -dimensional space are $2, 3$ and $6$ respectively, then the length of line segment is

6

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7

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9

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12

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Solution

The correct option is B $7$
Given projections are 2, 3 and 6

$∴$ AB $= \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2} + (z_{1} - z_{2})^{2}}$

$\Rightarrow A B = \sqrt{4 + 9 + 36} = \sqrt{49} = 7$ .

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