Question

30. Find the vector v with the given magnitude and the same direction as u.
||v|| = 3
u = (4,-4)

Answer 1

help?

Answer 2

Hint: Find the unit vector pointing in the same direction as u = (4, -4) and scale that unit vector by 3 to get your answer.

Answer 3

In the same direction means just find a unit vector in the direction of 4,-4 then multiply it by the magnitude, 3. So to do that divide by the magnitude:
\[||u||=\sqrt{16+16}=\sqrt{32}\]
Means:
\[\vec{w}_{\vec{u}}=\left< \frac{4}{\sqrt{32}},\frac{-4}{\sqrt{32}} \right>\]
So:
\[\vec{v}=3*\vec{w}_{\vec{u}}=\left< \frac{12}{\sqrt{32}},\frac{-12}{\sqrt{32}} \right>\]

Answer 4

is that all that i would put in my answer??

Answer 5

That's all I would. I don't know if you need to explain your procedure.

Answer 6

Also note that:
\[\vec{w}_{\vec{u}}\]
Denotes the unit vector in the u direction.

Answer 7

ok somehow i got the answer as \[\left(\begin{matrix}3\sqrt{2} \\8\end{matrix}\right)\]

Answer 8

i keep on thinking that its wrong...

Answer 9

But I just worked it all out above...check your work against mine...

Answer 10

ohh ok i see i didnt't finish my work. i had to write out v = part
does that have to be in that fraction form or decimal form?

Answer 11

thanks!!!!!!!!!! :D

Answer 12

I would do fraction.