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Numerade Educator

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Problem 17 Easy Difficulty

Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

$ a = \langle 1, -4, 1 \rangle , b = \langle 0, 2, -2 \rangle $

Answer

$$\cos ^{-1}\left(-\frac{5}{6}\right)=146^{\circ}$$

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Video Transcript

All right, So first, let's find the magnitude today. Ninety two today is one squared plus negative. Four squared plus one squared. That is rad eighteen. Just three, right, too magnitude of B zero squared plus two squared, plus native to squared. You're at a just to read, too. We also want to find the dog product, right. We're going to be using this formula, obviously, eh? B a b o sign. Okay, so the dot product is one time zero last night of two night of four times. Two last one times native to this is negative. Ten. Co signed data. Just a dot Be over, eh? B is the negative ten over three. Rad. Two times to read too. His negative turn over twelve. This is, uh we divide by to hear, Get negative. Not they does equal to co sign in verse. Uh, far native five, six. Okay, so turn that into a calculator. I divided by six negative of that coast on inverse. Yeah, one hundred forty six degrees