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How do you find the unit vector in the direction of the vector a = 3i + 4j?

1 Answer

A. S. Adikesavan

Aug 7, 2016

$\frac{1}{5} a$ $1/5 a$

Explanation:

The unit vector in the direction of

$a = r < cos θ, sin θ >$ $a = r < cos theta, sin theta>$ is

$(cos θ, sin θ)$ $(cos theta, sin theta)$ .

So, the unit vector is $\frac{1}{r} a$ $1/r a$ .

Here, it is $\frac{< 3, 4 >}{| < 3, 4 > |} = \frac{1}{\sqrt{3^{2} + 4^{2}}} a = \frac{1}{5} a$ $(<3, 4>)/|<3, 4>|=1/sqrt(3^2+4^2) a=1/5 a$

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