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Find the unit vector in the direction of v. v = -6.9i 3.3j

User Mmking
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Answer:


< -0.902, 0.431 >

Explanation:

The unit vector of any vector is the vector that has the same direction as the given vector, but simply with a magnitude of 1. Therefore, if we can find the magnitude of the vector at hand, and then multiply
(1)/(||v||), where ||v|| is the magnitude of the vector, then we can find the unit vector.

Remember the magnitude of the vector is nothing but the pythagorean theorem essentially, so it would be
\sqrt{(-6.9)^(2) +(3.3)^(2) } , which will be
√(58.5). Now let us multiply the vector by 1 over this value, and rationalize to make your math teacher happy.
< -6.9, 3.3 > * (1)/(√(58.5)) = < (-6.9√(58.5) )/(58.5) , (3.3√(58.5))/(58.5) >

You can put those values into your calculator to approximate and get


< -0.902, 0.431 >

You can always check the answer by finding the magnitude of this vector, and see that it is equal to 1.

Hope this helps

User Chris Down
by
8.9k points

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