Question

Find the unit vector which is parallel to the line
x-1/4=y-2/4=z -7/12

Answer 1

The line is given by the equation

$\dfrac{x-1}{4} = \dfrac{y-2}{4} = \dfrac{z-7}{12}.$

The denominators are the coordinates of the vector parallel to our line. But we can see that the norm of the vector isn't equal to 1. We should normalize it.

The norm of the vector is $\sqrt{4^2+4^2+12^2} = \sqrt{176} = 4\sqrt{11}.$

Therefore, the coordinates of the unit vector will be

$\left( \dfrac{4}{4\sqrt{11}}\,, \dfrac{4}{4\sqrt{11}}\,, \dfrac{12}{4\sqrt{11}},\right)$ that is equal to $\left( \dfrac{\sqrt{11}}{11}\,, \dfrac{\sqrt{11}}{{11}}\,, \dfrac{3\sqrt{11}}{{11}}\right)$ .