How would I find the angle between vectors $u$ & $v$ if $u$ $=$ $i$ + $4j$ & $v$ $=$ $-i$ + $2j$ ?

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How would I find the angle between vectors $u$ & $v$ if $u$ $=$ $i$ + $4j$ & $v$ $=$ $-i$ + $2j$ ?

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Answer 1 · 2015-10-08T23:54:59

I found $40.6^@$

Explanation:

I wold try using the Scalar (dot) Product between them:
We have: either (using the components):
$vecu*vecv=u_xv_x+u_yv_y=(1*-1)+(4*2)=-1+8=7$
or:
$vecu*vecv=|vecu|*|vecv|*cos(theta)$

where $theta$ is the angle between the two vectors:

$|vecu|=sqrt(1^2+4^2)=sqrt(17)$
$|vecv|=sqrt((-1)^2+2^2)=sqrt(5)$

Now we can use the two versions together:
$u_xv_x+u_yv_y=|vecu|*|vecv|*cos(theta)$

$7=sqrt(17)sqrt(5)cos(theta)$
$theta=cos^-1(7/(sqrt(17)sqrt(5)))=40.6^@$

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How would I find the angle between vectors $u$ & $v$ if $u$ $=$ $i$ + $4j$ & $v$ $=$ $-i$ + $2j$ ?

1 Answer

Explanation:

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