What is the projection of $< - 6, 3, 2 >$ $<-6,3,2 >$ onto $< 1, 4, - 3 >$ $<1,4,-3 >$ ?

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Answer 1 · 2017-01-09T20:12:11

No projection possible

The vector projection of $\to b$ $vecb$ over $\to a$ $veca$ is

$= \frac{\to a . \to b}{∥ ∥ \to a {∥ ∥}^{2}} \to a$ $=(veca.vecb)/(∥veca∥^2)veca$

The dot product is $\to a . \to b = ⟨ - 6, 3, 2 ⟩ . ⟨ 1, 4, - 3 ⟩ = - 6 + 12 - 6 = 0$ $veca.vecb=〈-6,3,2〉.〈1,4,-3〉=-6+12-6=0$

The vectors $\to a$ $veca$ and $\to b$ $vecb$ are perpendicular, it's not possible to make a projection.

What is the projection of <-6,3,2 ><−6,3,2><-6,3,2 > onto <1,4,-3 ><1,4,−3><1,4,-3 >?