Question

Write the direction cosines of the $x -$axis.

Answer 1

here, we are going to use the concept of direction cosines. Direction cosines of a line are the cosines of the angles made by the line with positive directions of the co-ordinate axes.

Complete step-by-step answer:
We know, direction cosines of a line making angle $\alpha$ with $x$-axis, $\beta$ with $y$-axis and $\gamma$ with $z$-axis are $l,m,n$ where $l = \cos \alpha ,m = \cos \beta ,n = \cos \gamma$
consider$x$-axis which makes an angle ${0^\circ }$ with the $x$-axis, ${90^\circ }$ with the $y -$ axis and ${90^\circ }$ with the $z -$axis
$\Rightarrow \alpha = {0^\circ },\beta = {90^\circ },\gamma = {90^\circ }$
Therefore, we have the direction cosines of $x$ -axis as given below
$l = \cos \alpha = \cos {0^\circ } = 1$
$m = \cos \beta = \cos {90^\circ } = 0$
$n = \cos \gamma = \cos {90^\circ } = 0$
Therefore, the cosines of $x$-axis are 1,0,0

Note: The values of cosines should be correctly calculated without any error. 0ne should also make a diagram if he/she has a problem while visualizing the line.