Question

Write the direction cosines of the \[x - \]axis.

Answer 1

Hint: 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.