Mathematics: Let v=-3sqrt2i-4sqrt2j, find a unit vector that points in the opposite direction

idkStep-by-step explanation:...

Let v=-3sqrt2i-4sqrt2j, find a unit vector that

Braxtonw875

13.03.2022

$\^v=-\frac{3}{5}i+\frac{4}{5}j$

Step-by-step explanation:

We have the following vector

$v=3\sqrt{2}i-4\sqrt{2}j$

First we calculate its magnitude

The magnitude of the vector v will be

$|v|=\sqrt{(3\sqrt{2})^2 + (4\sqrt{2})^2}\\\\|v|=\sqrt{9*2+16*2}\\\\|v|=\sqrt{18+32}\\\\|v|=5\sqrt{2}$

Now to create a unitary vector in the opposite direction to v, we divide the vector v between the negative of its magnitude

we call this new vector " $\^v$ "

$\^v=\frac{3\sqrt{2}}{-5\sqrt{2}}i-\frac{4\sqrt{2}}{-5\sqrt{2}}j$

$\^v=-\frac{3}{5}i+\frac{4}{5}j$

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