What is the projection of $< 6, - 6, 3 >$ $< 6 , -6 ,3 >$ onto $< 4, 9, 1 >$ $< 4, 9, 1>$ ?

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Answer 1 · 2017-01-21T11:20:12

The vector projection is $= - \frac{27}{98} < 4, 9, 1 >$ $=-27/98<4,9,1>$
The scalar projection is $= - \frac{27}{\sqrt{98}}$ $=-27/sqrt98$

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

$= \frac{\to a . \to b}{{∣ ∣ \to a ∣ ∣}^{2}} \cdot \to a$ $=(veca.vecb)/(|veca|^2)*veca$

The dot product is

$\to a . \to b = < 6, - 6, 3 > . < 4, 9, 1 \geq 24 - 54 + 3 = - 27$ $veca.vecb=<6,-6,3>.<4,9,1>=24-54+3=-27$

The modulus is

$∣ ∣ \to a ∣ ∣ = | < 4, 9, 1 > | = \sqrt{16 + 81 + 1} = \sqrt{98}$ $|veca|=|<4,9,1>|=sqrt(16+81+1)=sqrt98$

The vector projection is $= - \frac{27}{98} < 4, 9, 1 >$ $=-27/98<4,9,1>$

The scalar projection is

What is the projection of < 6 , -6 ,3 ><6,−6,3>< 6 , -6 ,3 > onto < 4, 9, 1><4,9,1>< 4, 9, 1>?