What is the projection of $< 6, - 4, 9 >$ $<6,-4,9 >$ onto $< 7, 8, 7 >$ $<7,8,7 >$ ?

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Answer 1 · 2017-02-04T07:44:38

The vector projection is $= \frac{73}{162} < 7, 8, 7 >$ $=73/162<7,8,7>$
The scalar projection $= \frac{73}{\sqrt{162}}$ $=73/sqrt162$

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

$\to a . \to b = < 7, 8, 7 > . < 6, - 4, 9 \geq 42 - 32 + 63 = 73$ $veca.vecb=<7,8,7>.<6,-4,9>=42-32+63=73$

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

$∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣ = | | < 7, 8, 7 > | | = \sqrt{49 + 64 + 49} = \sqrt{162}$ $||veca||=||<7,8,7>||=sqrt(49+64+49)=sqrt162$

The vector projection is

$= \frac{73}{162} < 7, 8, 7 >$ $=73/162<7,8,7>$

The scalar projection is

$\frac{\to a . \to b}{∣ ∣ ∣ ∣ \to a ∣ ∣ ∣ ∣} = \frac{73}{\sqrt{162}}$ $(veca.vecb)/(||veca||)=73/sqrt162$

What is the projection of <6,−4,9><6,-4,9 > onto <7,8,7><7,8,7 >?