Equation of the line passing through the point $$12$$,$$0$$,$$1and$$ making angles $$90$$°,$$45$$°,$$45$$°with axes respectively is

Question

Equation of the line passing through the point  $$12$$,$$0$$,$$1and$$ making angles  $$90$$°,$$45$$°,$$45$$°with axes respectively is

Infinity Learn · Accepted Answer

If  α,β,γare the angles made by a line ‘L’ with the coordinate axes in the positive direction then direction cosines are l,m,$$n=$$$$cos$$α,$$cos$$β,$$cos$$γHence, the direction cosines of the line which makes angles  $$90$$°,$$45$$°,$$45$$°with axes respectively is  $$0$$,$$12$$,$$12The$$ direction ratios of the above line are proportional to  $$0$$,$$1$$,$$1Therefore$$, the equation of the line passing through the point   $$12$$,$$0$$,$$1and$$ having the direction ratios  $$0$$,$$1$$,$$1is$$  $$2x$$−$$10=y$$−$$01=z$$−$$11$$

Equation of the line passing through the point $(\frac{1}{2}, 0, 1)$ and making angles $90 °, 45 °, 45 °$ with axes respectively is

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Equation of the line passing through the point 12,0,1and making angles 90°,45°,45°with axes respectively is

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Equation of the line passing through the point $(\frac{1}{2}, 0, 1)$ and making angles $90 °, 45 °, 45 °$ with axes respectively is