Question

The vector u has magnitude 6 and direction 330°. If vector v = =-u, then what is

the magnitude and direction of vector v? Write your direction in degrees in the
interval 0° 0 < 360°.

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Here we go ~

It's been given that :

`\qquad \sf  \dashrightarrow \: \vec{v} = - \vec{u}`

And magnitude of vector u is 6 units and with a direction 330°

And we are asked to find the magnitude and direction of vector v ~

So, let's get stated ~

As we can observe, vector v and vector u have equal magnitude because they have equal sign between them.

that is :

`\qquad \sf  \dashrightarrow \: | \vec{v} | = | \vec{u}|`

`\qquad \sf  \dashrightarrow \: | \vec{v}| = 6 \: units`

And the negative sign in the equation shows that the two vector have opposite directions or you can say they are anti-paralllel.

So, we can just rotate vector u by 180° to get vector v ~

`\qquad \sf  \dashrightarrow \: \hat{n} = 330 \degree - 180 \degree`

`\qquad \sf  \dashrightarrow \: \hat{n} = 150 \degree`

Conclusion :

• vector v has magnitude of 6 units and direction 150°