# What is the projection of #<2,4,3 ># onto #<-3,4,-1 >#?

The projection is

In this case,

The product that dots are

The projection of a vector is

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The projection of (\mathbf{v}) onto (\mathbf{u}) is given by:

[ \text{proj}_{\mathbf{u}}(\mathbf{v}) = \frac{\mathbf{v} \cdot \mathbf{u}}{|\mathbf{u}|^2} \mathbf{u} ]

Given (\mathbf{v} = \langle 2, 4, 3 \rangle) and (\mathbf{u} = \langle -3, 4, -1 \rangle), the projection of (\mathbf{v}) onto (\mathbf{u}) is:

[ \text{proj}_{\mathbf{u}}(\mathbf{v}) = \frac{\langle 2, 4, 3 \rangle \cdot \langle -3, 4, -1 \rangle}{| \langle -3, 4, -1 \rangle |^2} \langle -3, 4, -1 \rangle ]

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