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University of North Texas

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Problem 10 Easy Difficulty

Find $ a \cdot b $.

$ \mid a \mid = 80 $ , $ \mid b \mid = 50 $ , the angle between $ a $ and $ b $ is $ \frac{3 \pi}{4} $

Answer

$-2000 \sqrt{2}$

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Video Transcript

So this case for us to find the dot product, the form what are going to want to use is the one that I have on the board where it is going to be the dot product of A and B is the magnitudes of each of those multiplied together times the cosine of the angle between them. And we have all that already because they just give it to us. So we just need to come over here and plug all that in now. So we know that the magnitude of a is 80. The magnitude of the is 50. And then, you know, the angle between them is three pi fourth. So now we just multiply everything together. Uh, so 80? Yeah. Times 40 would be armed up 40 80 times. 50 should be 4000. Co sign of three pi force. Well, that is where co sign is negative. It would be negative. Route two or two and then simplifying the two in the 4000 would give us 2000, so this would be negative 2000 route to. So this is going to be our product