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Compute the quantities in Exercises $1-8$ using the vectors$$\mathbf{u}=\left[\begin{array}{r}{-1} \\ {2}\end{array}\right], \quad \mathbf{v}=\left[\begin{array}{l}{4} \\ {6}\end{array}\right], \quad \mathbf{w}=\left[\begin{array}{r}{3} \\ {-1} \\ {-5}\end{array}\right], \quad \mathbf{x}=\left[\begin{array}{r}{6} \\ {-2} \\ {3}\end{array}\right]$$$\frac{1}{\mathbf{u} \cdot \mathbf{u}} \mathbf{u}$

$\left[\begin{array}{r}{-\frac{1}{5}} \\ {\frac{2}{5}}\end{array}\right]$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 1

Inner Product, Length, and Orthogonality

Vectors

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So we're giving the vector you and we want to compute. Um, the following. Ah. So we first when you find you, don't you? So you got you. We just take the corresponding first entries. Multiply on, and I have the corresponding second entries. So we have negative one times. Negative one, just one plus two times two is four. So that gives us five. So this quandary on the outside here is just, uh, won over five. So we want to take 1/5 of the factory. So when we do that, we just divide each entry by five. So we get negative. 1/5 and 2/5. Not sorry, sir.

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