Question #184049

If 1, 1/2, 0 are direction ratios of a line, then the line makes an angle of 90° with the x-axis, an angle of 60° with the y-axis, and is parallel to the z-axis. State whether true or false, also give reason for your answer.


1
Expert's answer
2021-05-04T13:14:35-0400

We have given the direction ratios 1,12,01, \dfrac{1}{2}, 0


Also we have given the angles 90,60,090 ^\circ, 60^ \circ, 0^ \circ


We know,

cosα=aa2+b2+c2cos\alpha = \dfrac{a}{\sqrt{a^2+b^2+c^2}}


cosα=154cos \alpha = \dfrac{1}{\sqrt{\dfrac{5}{4}}} =25\dfrac{2}{\sqrt5}


cosβ=ba2+b2+c2cos\beta = \dfrac{b}{\sqrt{a^2+b^2+c^2}}


cosβ=1254cos \beta = \dfrac{\dfrac{1}{2}}{\sqrt{\dfrac{5}{4}}} = 15\dfrac{1}{\sqrt5}


cosγ=ca2+b2+c2cos\gamma = \dfrac{c}{\sqrt{a^2+b^2+c^2}} = 0


Hence, the calculated values of direction cosine does not match with the given values.

Therefore, it is False .



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