How do you find the vector v with the given magnitude of 5 and in the same direction as $u=<3,3>$ ?

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Answer 1 · 2017-05-03T18:30:27

Please see the explanation.

Given: $|vecv|= 5$

We know the formula for the magnitude

$|vecv|= sqrt(x^2+y^2)" [1]"$

This problem is made simple by the fact that the x component of the vector $vecu$ is the same as the y component.

$y = x$

Substitute x for y into equation [1]:

$|vecv|= sqrt(x^2+x^2)" [2]"$

Substitute 5 for the magnitude into equation [2]:

$5= sqrt(x^2+x^2)$

$25= 2x^2$

$25/2=x^2$

$x = 5sqrt2/2$

We know that $y = x$ :

$y = 5sqrt(2)/2$

The vector is $< 5sqrt(2)/2, 5sqrt(2)/2 >$

How do you find the vector v with the given magnitude of 5 and in the same direction as u=<3,3>u=<3,3>?