Answer to Question #184049 in Analytic Geometry for Garima Ahlawat

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, \\dfrac{1}{2}, 0"


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


We know,

"cos\\alpha = \\dfrac{a}{\\sqrt{a^2+b^2+c^2}}"


"cos \\alpha = \\dfrac{1}{\\sqrt{\\dfrac{5}{4}}}" ="\\dfrac{2}{\\sqrt5}"


"cos\\beta = \\dfrac{b}{\\sqrt{a^2+b^2+c^2}}"


"cos \\beta = \\dfrac{\\dfrac{1}{2}}{\\sqrt{\\dfrac{5}{4}}}" = "\\dfrac{1}{\\sqrt5}"


"cos\\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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