Question

Write the direction cosines of $x$-axis.

Answer 1

Say ${(x}_1,0,0),{(x}_2,0,0)$ be two points on x axis

DR's of a line is given by subtracting position vectors.

DR's of x axis is ${(x}_1-x_2,0,0)$

DC's of any vector are obtained by dividing the vector with it's magnitude

${|x}_1-x_2|={(x_1-x_2)}^2+0^2+0^2$

$D{C}^{\prime }s=\frac{{(x}_1-x_2)\hat{i}}{{|x}_1-x_2|}=\pm (1,0,0)$

DC's of x axis are $(1,0,0),(-1,0,0)$