Question

For v=-3i-7j, find the unit vector in the same direction of v, and write your answer as a linear combination of the standard unit vectors I and j.

Answer 1

Answer:

$-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}$

Step-by-step explanation:

The given vector is:

v = -3i-7j

The unit vector is found by dividing the vector by its magnitude

$Unit\ vector\ of\ v=\frac{v}{||v||}$

We have to find the magnitude first

So,

$||v||=\sqrt{(-3)^{2} +(-7)^{2}}\\ =\sqrt{9+49}\\ =\sqrt{58}$

The unit vector is:

$\frac{-3i-7j}{\sqrt{58} } \\=>-\frac{3i}{\sqrt{58}}-\frac{7j}{\sqrt{58}}\\=>(-\frac{3i}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}}) -(\frac{7j}{\sqrt{58}}*\frac{\sqrt{58}}{\sqrt{58}})\\=>-\frac{3\sqrt{58} i}{{58}}-\frac{7\sqrt{58}j}{{58}}$

Therefor the last option is the correct answer ..