What is the projection of $< 4, 0, 1 >$ $<4,0,1 >$ onto $< 6, - 3, 7 >$ $<6,-3,7 >$ ?

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Answer 1 · 2016-12-23T14:50:13

The answer is $= \frac{31}{94} ⟨ 6, - 3, 7 ⟩$ $=31/94〈6,-3,7〉$

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

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

The dot product is $= \to a . \to b$ $=veca.vecb$
$= ⟨ 4, 0, 1 ⟩ . ⟨ 6, - 3, 7 ⟩ = (24 + 0 + 7) = 31$ $=〈4,0,1〉.〈6,-3,7〉=(24+0+7)=31$

The modulus of $\to a$ $veca$ is $= ∥ \to a ∥ = ∥ ⟨ 6, - 3, 7 ⟩ ∥ ∥$ $=∥veca∥=∥〈6,-3,7〉∥$

$= \sqrt{36 + 9 + 49} = \sqrt{94}$ $=sqrt(36+9+49)= sqrt94$

The vector projection is $= \frac{31}{94} ⟨ 6, - 3, 7 ⟩$ $=31/94〈6,-3,7〉$

What is the projection of <4,0,1><4,0,1 > onto <6,−3,7><6,-3,7 >?