(B) Let the projections of the line segment on the $x, y$ and $z-$ axes be $p_x = 2$,$p_y = 3$,and $p_z = 6$ respectively.The length of the line segme

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(B) Let the projections of the line segment on the $x, y$ and $z-$ axes be $p_x = 2$,$p_y = 3$,and $p_z = 6$ respectively.The length of the line segment $L$ in $3-$ dimensional space is given by the formula $L = \sqrt{p_x^2 + p_y^2 + p_z^2}$.Substituting the given values,we get $L = \sqrt{2^2 + 3^2 + 6^2}$.$L = \sqrt{4 + 9 + 36}$.$L = \sqrt{49}$.$L = 7$.Therefore,the length of the line segment is $7$.

Class 12 Mathematics Three Dimensional Geometry System of co-ordinates, Direction cosines and direction ratios, Projection

Easy

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 the line segment is

JEE MAIN 2013 All JEE MAIN

A
$12$
B
$7$
C
$9$
D
$6$

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System of co-ordinates, Direction cosines and direction ratios, Projection

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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 the line segment is

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