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Compute the orthogonal projection of $\left[\begin{array}{l}{1} \\ {7}\end{array}\right]$ onto the line through $\left[\begin{array}{r}{-4} \\ {2}\end{array}\right]$ and the origin.

$\left[\begin{array}{c}{-2} \\ {1}\end{array}\right]$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 2

Orthogonal Sets

Vectors

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this question wants us to find the projection of you onto the so Remember that to find the projection onto V of a vector, you you just take the dot products you dot v divide by the magnitude squared of the and then you just distribute that into the back turvey and we can find all of these things. So you doubt the would be negative four plus 14. The magnitude of the squared would be just the sum of the squared components. So four squared plus two squared, and then our vector V is just for or negative for two. So then we'd get 10 divided by 20 times negative for two or one half times negative for two, giving us a projection vector of negative too well.

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