Answer to Question #184049 in Analytic Geometry for Garima Ahlawat

Question

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.

Answer 1

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 .