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You can ask questions about our review for quiz 1 by posting them here!
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Archived May, 2026.
Questions on Review for Quiz 1
User 018
Is there an intuitive method of deriving the formula for the projection of vectors? I am struggling to remember it and curious if anyone has any tips or tricks.
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@User 053 I guess the formula is
\text{proj}_{\vec{u}}\vec{v} = \frac{\vec{u}\cdot\vec{v}}{\vec{u}\cdot\vec{u}}\vec{u}.
Here's how I think of this:
First, this is a scalar((\vec{u}\cdot\vec{v})/{(\vec{u}\cdot\vec{u})}) times a vector \vec{u}. Here's how I think of it:
- The projection is onto \vec{u} so we should should have some scalar *\vec{u}. That's where that part comes from.
- I think it shouldn't be too hard to remember that the scalar is a ratio of dot products of the vectors involved. If you remember that's more \vec{u}\text{s} than \vec{v}\text{s}, then there's not too many choices left.
If you really want to understand the derivation, it comes from
\frac{\vec{u}\cdot\vec{v}}{\vec{u}\cdot\vec{u}}\vec{u} = \frac{\vec{u}\cdot\vec{v}}{\|\vec{u}\|} \frac{\vec{u}}{\|\vec{u}\|}.
The first part is the magnitude of the projection, which can be derived using a little trigonometry, and the second is the unit vector pointing the direction of \vec{u}.
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