What is the projection of $< 8, 2, 1 >$ $<8,2,1 >$ onto $< 9, 6, 3 >$ $<9,6,3 >$ ?

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Answer 1 · 2016-12-21T07:18:55

The answer is $= \frac{87}{126} ⟨ 9, 6, 3 ⟩$ $=87/126〈9,6,3〉$

The vector 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 $\to a . \to b = ⟨ 8, 2, 1 ⟩ . ⟨ 9, 6, 3 ⟩$ $veca.vecb=〈8,2,1〉.〈9,6,3〉$

$= (72 + 12 + 3) = 87$ $=(72+12+3)=87$

The modulus of $\to a$ $veca$ is $= ∥ \to a ∥ = ∥ ⟨ 9, 6, 3 ⟩ ∥ ∥$ $=∥veca∥=∥〈9,6,3〉∥$

$= \sqrt{81 + 36 + 9} = \sqrt{126}$ $=sqrt(81+36+9)=sqrt126$

The vector projection is $= \frac{87}{126} ⟨ 9, 6, 3 ⟩$ $=87/126〈9,6,3〉$

What is the projection of <8,2,1><8,2,1 > onto <9,6,3><9,6,3 >?