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Numerade Educator

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Problem 19 Easy Difficulty

Find $ a + b , 4a + 2b , \mid a \mid $, and $ \mid a - b \mid $.

$ a = \langle -3, 4 \rangle , b = \langle 9, -1 \rangle $

Answer

$$
|\mathbf{a}-\mathbf{b}|=\sqrt{(-12)^{2}+5^{2}}=\sqrt{144+25}=\sqrt{169}=13
$$

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Video Transcript

for the given problem, we want to find A plus B. For a plus to be absolute value of A or the magnitude of A and the magnitude of a minus B. So A plus B is going to be If we have negative 34 as are A. And we know that be Is equal to 9 -1 with vector edition. How it works is that we just add the components together. So we're going to add our components and we're going to get six three and that will be our answer. And then we can also look at um since for a place to be is very similar um let's look at the magnitude because how you do magnitude as you take the component squared plus the other component squared. So we'll get a negative three square that's nine Plus the other component squared. four square to 16. So we get the square root of 9-plus 16. That's the square root of 25. So our final answer is going to equal five.