Question

Just checking.
\[\vec{u}=(-2,-4,-3), \vec{v}=(-1,-3,-4); Proj_v\vec{u}\]

Answer 1

\[\frac{\langle \vec{u},\vec{v} \rangle}{\langle \vec{v},\vec{v} \rangle}\vec{v}=\frac{\langle (-2,-4,-3),(-1,-3,-4) \rangle}{\langle (-1,-3,-4),(-1,-3,-4) \rangle}\vec{v}\\
\implies \frac{2+12+12}{1+9+16}\vec{v}\implies \frac{26}{26}\vec{v}\implies(-1,-3,-4)\]Which just seems too good to be true.

Answer 2

isnt that just the dot product xD

Answer 3

Project \(\vec{u}\) onto \(\vec{v}\).

Answer 4

The wonders of notation... they seem to nver agree on a single notation in Linear.

No, the dot would be an orthogonal check.

Answer 5

or instead of that just do U.(V/|V|)
where you are taking the unit direction vector of V that way
U.Unit vector = U cos@ or component of U along V

Answer 6

Projection is an orthornormal basis for a subspace...

Answer 7

what does that mean? so projection is the component of U on V