If the projections of the line segment AB¯ on the $$yz-plane$$, $$zx-plane$$, $$xy-$$ plane are $$160$$,$$153$$ and $$5$$ respectively, then the projection of AB¯on the $$z-axis$$ is

Question

If the projections of the line segment AB¯ on the $$yz-plane$$, $$zx-plane$$, $$xy-$$ plane are  $$160$$,$$153$$  and  $$5$$ respectively, then the projection of AB¯on the $$z-axis$$ is

Infinity Learn · Accepted Answer

The projection of the line segment AB¯ on the $$yz-plane$$ is  $$y2$$−$$y12+z2$$−$$z12=160The$$ projection of the line segment AB¯on the $$zx-plane$$ is  $$z2$$−$$z12+x2$$−$$x12=153The$$ projection of the line segment AB¯on the $$xy-plane$$ is $$x2$$−$$x12+y2$$−$$y12=5It$$ implies that $$x2$$−$$x12+y2$$−$$y12+z2$$−$$z12=169Hence$$,$$z2$$−$$z12=169$$−$$25=144Apply$$ square root on both $$sidesz2$$−$$z1=12$$ , this is the length of the projection ofAB¯  on $$z-$$ axis.

If the projections of the line segment $\bar{A B}$ on the $y z -$ plane, $z x -$ plane, $x y -$ plane are $\sqrt{160}, \sqrt{153} and 5$ respectively, then the projection of $\bar{A B}$ on the $z -$ axis is

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If the projections of the line segment AB¯ on the yz-plane, zx-plane, xy- plane are 160,153 and 5 respectively, then the projection of AB¯on the z-axis is

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If the projections of the line segment $\bar{A B}$ on the $y z -$ plane, $z x -$ plane, $x y -$ plane are $\sqrt{160}, \sqrt{153} and 5$ respectively, then the projection of $\bar{A B}$ on the $z -$ axis is