The projections of a line on the coordinate a | vedclass

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(A) Let $d$ be the length of the line and $l, m, n$ be its direction cosines.The projections of the line on the $x, y,$ and $z$ axes are given by $dl,

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$7$

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(A) Let $d$ be the length of the line and $l, m, n$ be its direction cosines.The projections of the line on the $x, y,$ and $z$ axes are given by $dl, dm,$ and $dn$ respectively.Given: $dl = 2, dm = 3, dn = 6$.We know that the sum of the squares of the direction cosines is $l^2 + m^2 + n^2 = 1$.Squaring and adding the given projections,we get:$(dl)^2 + (dm)^2 + (dn)^2 = 2^2 + 3^2 + 6^2$$d^2(l^2 + m^2 + n^2) = 4 + 9 + 36$$d^2(1) = 49$$d = \sqrt{49} = 7$.Thus,the length of the line is $7$.

The projections of a line on the coordinate axes are $2, 3, 6$. Then the length of the line is

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