What is the projection of $< 5, 6, 1 >$ $<5,6,1 >$ onto $< 8, - 5, 1 >$ $<8,-5,1 >$ ?

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What is the projection of $< 5, 6, 1 >$ $<5,6,1 >$ onto $< 8, - 5, 1 >$ $<8,-5,1 >$ ?

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Answer 1 · 2016-02-15T13:48:05

$\to C = < \frac{88}{90}, - \frac{55}{90}, \frac{11}{90} >$ $vec C= <88/90 ,-55/90,11/90>$

Explanation:

$\to A = < a, b, c >$ $vec A= < a,b,c >$
$\to B = < d, e, f >$ $vec B= < d,e,f >$
$Projection of A onto B is given as :$ $"Projection of A onto B is given as :"$
$\to C = \frac{\to A . \to B}{{∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣}^{2}} \to B$ $vec C= (vec A .vec B)/(||vec B||^2)vec B$
$\to A \cdot \to B = a . d + b . e + c . f = 40 - 30 + 1 = 11$ $vec A* vec B=a.d+b.e+c.f=40-30+1=11$
$magnitude of \to B = \sqrt{64 + 25 + 1} = \sqrt{90}$ $"magnitude of "vec B=sqrt (64+25+1)=sqrt 90$
$\to C = \frac{11}{90} < 8, - 5, 1 >$ $vec C=11/90<8,-5,1>$
$\to C = < \frac{88}{90}, - \frac{55}{90}, \frac{11}{90} >$ $vec C= <88/90 ,-55/90,11/90>$

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What is the projection of $< 5, 6, 1 >$ $<5,6,1 >$ onto $< 8, - 5, 1 >$ $<8,-5,1 >$ ?

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Explanation:

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What is the projection of <5,6,1><5,6,1 > onto <8,−5,1><8,-5,1 >?

1 Answer

Explanation:

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What is the projection of $< 5, 6, 1 >$ $<5,6,1 >$ onto $< 8, - 5, 1 >$ $<8,-5,1 >$ ?