Vectors, please check :)

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Vectors, please check :)

Mathematics
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A few simple questions! u= <-2,4> v=5i-3i 1) find 6u-v = <-17,21> 2) fine a unit vector in the direction of v this one i'm ont sure about 3) graph u, v, and u-v with initial points of origin. again, i have an idea but im not sure
look there is a typo ``` v=5i-3i ```
sowire v= 5i-3j

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Other answers:

6*4 - (-3) = ?
27
why those numbers?
u= <-2, 4> v=5i-3j = <5, -3> 6u - v = ?
<-17,21>
can you show work for how you got 21 ?
6u = <-12,24> v= <5,-3> (-12-5), (24-3) = <-17,21>
check again
is it 24-3 or 24-(-3) ?
ooh right rigt.
soo.. <-17,25> ?
lol sorry, *27
yes
fabulous :)
part b then
what do u know about unit vector ?
er, is this where I use cos and sin?
or multiplying by scalar?
Idk :/
It's the angle formed by the vector and x.
unit vector is just a vector whose magnitude is 1 and points in the same direction
what is the magnitude of vector v ?
er \[\sqrt{25+9}\]
yes what do you need to do to make it 1 ?
What do you mean?
what do you need to do to \(\sqrt{25+9}\) to make it \(1\) ?
dividing by \(\sqrt{25+9}\) produces \(1\), yes ?
yeah dividing it by itself
so the unit vector is simply : \[\large \dfrac{v}{\|v\|}\]
dividing the original vector by its magnitude gives the unit vector
\[\frac{ 5i -3j}{ \sqrt{34} }\]
?
Yes thats the unit vector in the direction of \(v\)
so that would be the final answer? :)
yes
yay! Part c then ^-^
graph the vectors
|dw:1433398194050:dw|
To graph the vector u= <-2,4> first plot the point (-2, 4) and draw an arrow from (0,0) to (-2,4)
|dw:1433398294843:dw|
(-7,7) isn't on the graph :P
|dw:1433398431757:dw|
yeah u-v = <-7, 7> is not on this graph but i see you get how to draw the vectors
don't forget to put arrow at the final point
okies! thanks :)
np

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