What is the projection of $< - 2, 2, 5 >$ $<-2,2,5 >$ onto $< 1, 6, 9 >$ $<1,6,9 >$ ?

Question

1391 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-19T10:33:58

The answer is $= \frac{55}{118} ⟨ 1, 6, 9 ⟩$ $=55/118〈1,6,9〉$

The projection of $\to b$ $vecb$ onto $\to a$ $veca$ is

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

The dot product is $= ⟨ - 2, 2, 5 ⟩ . ⟨ 1, 6, 9 ⟩$ $=〈-2,2,5〉.〈1,6,9〉$

$= (- 2 + 12 + 45)$ $=(-2+12+45)$

$= 55$ $=55$

The modulus of $\to a$ $veca$

$= ∥ ⟨ 1, 6, 9 ⟩ ∥$ $=∥〈1,6,9〉∥$

$= \sqrt{1 + 36 + 81} = \sqrt{118}$ $=sqrt(1+36+81)=sqrt118$

Therefore,

the projection is

$= \frac{55}{118} ⟨ 1, 6, 9 ⟩$ $=55/118〈1,6,9〉$

What is the projection of <−2,2,5><-2,2,5 > onto <1,6,9><1,6,9 >?