If a line passing through origin is inclined at $$60$$°and $$45$$°to $$X-and$$ $$Y-axes$$ respectively, Then the angle at which it is inclined to $$Z-axis$$, is

Question

If a line passing through origin is inclined at $$60$$°and $$45$$°to $$X-and$$ $$Y-axes$$ respectively, Then the angle at which it is inclined to $$Z-axis$$, is

Infinity Learn · Accepted Answer

If α,β,γ are the angles made by a line ‘L’ with the coordinate axes in the positive direction then $$cos2$$α$$+cos2$$β$$+cos2$$γ$$=1Here$$,α$$=60$$°,β$$=45$$°Hence,$$cos260$$°$$+cos245$$°$$+cos2$$γ$$=1$$                     $$14+12+cos2$$γ$$=1$$                                  $$cos2$$γ$$=14$$                                 $$cos$$γ$$=$$±$$12Therefore$$,γ$$=60$$° or $$120$$°

If a line passing through origin is inclined at $60 °$ and $45 °$ to $X -$ and $Y -$ axes respectively, Then the angle at which it is inclined to $Z -$ axis, is

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If a line passing through origin is inclined at 60°and 45°to X-and Y-axes respectively, Then the angle at which it is inclined to Z-axis, is

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Ready to Test Your Skills?

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If a line passing through origin is inclined at $60 °$ and $45 °$ to $X -$ and $Y -$ axes respectively, Then the angle at which it is inclined to $Z -$ axis, is