What is the projection of $< - 3, 5, - 9 >$ $<-3,5,-9 >$ onto $< 2, - 1, 4 >$ $<2,-1,4 >$ ?

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Answer 1 · 2017-02-14T10:46:09

The vector projection is $= - \frac{47}{21} < 2, - 1, 4 >$ $=-47/21<2,-1,4>$
The scalar projection is $= - \frac{47}{\sqrt{21}}$ $=-47/sqrt21$

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

$\to a . \to b = < 2, - 1, 4 > . < - 3, 5, - 9 \geq - 6 - 5 - 36 = - 47$ $veca.vecb= <2,-1,4>.<-3,5,-9>=-6-5-36=-47$

The modulus of $\to a$ $veca$ is

$= | | < 2, - 1, 4 > | | = \sqrt{4 + 1 + 16} = \sqrt{21}$ $=||<2,-1,4>|| =sqrt(4+1+16)=sqrt21$

The vector projection is

$= - \frac{47}{21} < 2, - 1, 4 >$ $=-47/21<2,-1,4>$

The scalar projection is

$= \frac{\to a . \to b}{∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣} = - \frac{47}{\sqrt{21}}$ $=(veca.vecb)/||veca||=-47/sqrt21$

What is the projection of <−3,5,−9><-3,5,-9 > onto <2,−1,4><2,-1,4 >?