Question

Help with vectors

Answer 1

Write v as the sum of two vector components if v = i + 3j and w =-2i + 5j.

Answer 2

(i*-2)+(3*5)
-2+15
13=v*w

Answer 3

v is already written as the sum of two vector components

Answer 4

the horizontal component is 1 and the vertical is 3

Answer 5

yes but we have to get v1 from this

Answer 6

then v2=v-v1

Answer 7

thats what it means by components

Answer 8

So you want to find the sum of v and w?

Answer 9

well we have to find the projection of v onto w first

Answer 10

so with this so far we know \[\frac{ 13 }{ ||(-2,5)||^2 }(-2i,5j)\]

Answer 11

\[\frac{ 13 }{ \sqrt29 }=\frac{ 13 }{ 29 }(-2)\]

Answer 12

(-26/29i, 65/29j)=v1

Answer 13

So you projection is \[<\frac{ -26 }{ \sqrt{29} },\frac{ 65 }{ \sqrt{29} }\]

Answer 14

yes

Answer 15

well no not sqrt 29

Answer 16

oh yeah

Answer 17

sqrt 29 gets canceled at sqrt29^2

Answer 18

v2=(i+3j)-(-26/29i, 65/29j)

Answer 19

actually no i did that wrong

Answer 20

Wouldn't it be 55/29 i+22/29 j

Answer 21

55/29i+22/20j

Answer 22

yes that is right

Answer 23

v2=55/29i + 22/20j

Answer 24

now to check v1*v2

Answer 25

(-26/29i, 65/29j) * (55/29i+22/20j)

Answer 26

Lord so much multiplication

Answer 27

basically it works out to

-1430/841+1430/841=0 and we are good this is correct :D

Answer 28

cool