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Numerade Educator

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Problem 21 Easy Difficulty

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

$ a = 4i - 3j + 2k , b = 2i - 4k $

Answer

$$
\begin{array}{l}{\|\overline{a}-\overline{b}\|} \\ {=\sqrt{(\overline{a}-\overline{b})_{i}^{2}+(\overline{a}-\overline{b})_{j}^{2}+(\overline{a}-\overline{b})_{k}^{2}}} \\ {=\sqrt{2^{2}+(-3)^{2}+6^{2}}} \\ {=\sqrt{49}} \\ {=7}\end{array}
$$

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Video Transcript

Yeah. For the given problem, we want to evaluate some of the functions knowing that A. Is going to be vector for negative 32 Mhm. And B will be the victor two negative four or 20 negative for so some of these factors A plus B is going to be four plus 26 maybe a three plus zero standing free. And then to minus four is going to be negative too. So that the sum of the vectors in the components. Now let's look at how to calculate the magnitude. It's gonna be very similar to how it was before the square root of fourth grade, which is 16 Plastic Square root of negative surplus. A negative free spread which is nine. Um so it's gonna be 25 And then 25-plus 4. So we'll have route 29 as the magnitude.