Given $${\mathbf a} = (-10, -8, 9) $$and $${\mathbf b} = (4, 5, 8) $$
Can someone please define what it means to find the orthogonal projection of b onto a?
Also what is the formula for computing the orthogonal projection of b onto a?
Thank you in advance!
EDIT:
Using the formula for b projection a I get the vectors:
$$(80/245, 64/245, -72/245)$$
But that's incorrect for the orthogonal projection.
[Math] Find the orthogonal projection of b onto a
multivariable-calculusvectors
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Best Answer
The orthogonal projection of a vector $b$ onto a vector $a$ is its component in the direction of $a$. The formula for this is:
$$\mathrm{proj \,\textbf{b}_{\textbf{a}}} = \frac{a \cdot b}{a \cdot a}a$$
This should intuitively make sense. Consider the definition of the dot product in geometric terms, and notice that the projection must be in the direction of $a$.
Now plug your vectors into this formula and get an answer.