Question

Q3 Projection 3 Points Find the orthogonal projection of the vector $x = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$ onto the vector $y = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$ Hint: The result should be a vector that is in the same direction as y but with a different magnitude. Note: these vectors are not unit vectors and so you will have to amend slightly the equation from the video. The following definition will be useful for your derivation, it will also help you to draw a picture $x^T y = ||x|| ||y|| \cos(\theta)$ where $\theta$ is the angle between the vectors and the magnitudes are given by $||x|| = \sqrt{x^T x}$

          Q3 Projection
3 Points
Find the orthogonal projection of the vector

$x = \begin{bmatrix} 1 \\ 1 \end{bmatrix}$

onto the vector

$y = \begin{bmatrix} 1 \\ 2 \end{bmatrix}$

Hint: The result should be a vector that is in the same direction as y but with a different magnitude.
Note: these vectors are not unit vectors and so you will have to amend slightly the equation from the
video. The following definition will be useful for your derivation, it will also help you to draw a picture

$x^T y = ||x|| ||y|| \cos(\theta)$

where $\theta$ is the angle between the vectors and the magnitudes are given by

$||x|| = \sqrt{x^T x}$

q3 projection 3 points find the orthogonal projection of the vector x beginbmatrix 1 1 endbmatrix onto the vector y beginbmatrix 1 2 endbmatrix hint the result should be a vector that is in 46883

Added by Melissa N.

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