(A) Let the projections of the line segment on the $x, y, z$ axes be $a = 12$,$b = 4$,and $c = 3$.The length of the line segment $L$ is given by the f

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(A) Let the projections of the line segment on the $x, y, z$ axes be $a = 12$,$b = 4$,and $c = 3$.The length of the line segment $L$ is given by the formula $L = \sqrt{a^2 + b^2 + c^2}$.Substituting the values: $L = \sqrt{12^2 + 4^2 + 3^2} = \sqrt{144 + 16 + 9} = \sqrt{169} = 13$.The direction cosines $(l, m, n)$ are given by $l = a/L$,$m = b/L$,and $n = c/L$.Therefore,$l = 12/13$,$m = 4/13$,and $n = 3/13$.Thus,the length is $13$ and the direction cosines are $$.

Class 12 Mathematics THREE DIMENSIONAL GEOMETRY System of co-ordinates, Direction cosines and direction ratios, Projection

Easy

The projections of a line segment on the $x, y, z$ axes are $12, 4, 3$ respectively. Find the length and the direction cosines of the line segment.

A
$13, < 12/13, 4/13, 3/13 >$
B
$19, < 12/19, 4/19, 3/19 >$
C
$11, < 12/11, 14/11, 3/11 >$
D
None of these

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

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The projections of a line segment on the $x, y, z$ axes are $12, 4, 3$ respectively. Find the length and the direction cosines of the line segment.

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