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Numerade Educator

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Problem 20 Easy Difficulty

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

$ a = 5i + 3j , b = -i - 2j $

Answer

$$
|\mathbf{a}-\mathbf{b}|=\sqrt{6^{2}+5^{2}}=\sqrt{36+25}=\sqrt{61}
$$

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Video Transcript

So for this problem we are given that A. Is going to equal the vector um five I plus three J. We're just going to put this in component notation 53 And then the b vector is going to equal negative i minus two J. So putting in component notification will get negative one negative two. So then when we add these together um A vector plus the B factor will end up getting that A. Plus we equals 5 -1, which is 24 And then 3 -2 which is gonna be one. That's a. Plus the vector. And then we can also calculate other things. Let's do the magnitude of a. So we see that the magnitude of a is going to equal the square root of five square. So Square 25. What's The Square Root of 9? Okay, now, between the square root of 34 as our final answer.