What is the projection of $< - 3, 6, 7 >$ $< -3, 6, 7>$ onto $< 5, - 3, 8 >$ $< 5, -3, 8>$ ?

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Answer 1 · 2017-02-05T10:48:44

The vector projection is $= \frac{53}{98} < 5, - 3, 8 >$ $=53/98<5,-3,8>$
The scalar projection is $= \frac{53}{\sqrt{98}}$ $=53/sqrt98$

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

$\to a . \to b = < 3, 6, 7 > . < 5, - 3, 8 \geq 15 - 18 + 56 = 53$ $veca.vecb=<3,6,7>.<5,-3,8>=15-18+56=53$

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

$∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ = | | < 5, - 3, 8 > | | = \sqrt{25 + 9 + 64} = \sqrt{98}$ $||veca||=||<5,-3,8>||=sqrt(25+9+64)=sqrt98$

The vector projection is

$= \frac{53}{98} < 5, - 3, 8 >$ $=53/98<5,-3,8>$

The scalar projection is

$\frac{\to a . \to b}{∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣} = \frac{53}{\sqrt{98}}$ $(veca.vecb)/(||veca||)=53/sqrt98$

What is the projection of < -3, 6, 7><−3,6,7>< -3, 6, 7> onto < 5, -3, 8><5,−3,8>< 5, -3, 8>?