What is the projection of $< - 5, 2, 8 >$ $<-5,2,8>$ onto $< 8, - 3, 3 >$ $<8,-3,3 >$ ?

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What is the projection of $< - 5, 2, 8 >$ $<-5,2,8>$ onto $< 8, - 3, 3 >$ $<8,-3,3 >$ ?

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Answer 1 · 2016-03-12T19:29:08

$\to C = - \frac{11}{41} (8 ˆ i - 3 ˆ j + 3 ˆ k)$ $vec C=-11/41(8 hat i-3 hat j+3 hat k)$

Explanation:

$\to A = - 5 ˆ i + 2 ˆ j + 8 ˆ k \to B = 8 ˆ i - 3 ˆ j + 3 ˆ k$ $vec A=-5 hat i+2 hat j+8 hat k" "vec B=8 hat i-3 hat j+3 hat k$
$A \cdot B = - 5 \cdot 8 + 2 (- 3) + 8 \cdot 3 = - 40 - 6 + 24 = - 22$ $A*B=-5*8+2(-3)+8*3=-40-6+24=-22$
$| | B | | = \sqrt{8^{2} + {(- 3)}^{2} + 3^{2}} = \sqrt{64 + 9 + 9} = \sqrt{82}$ $||B||=sqrt(8^2+(-3)^2+3^2)=sqrt(64+9+9)=sqrt82$
$the projection of \to A onto \to B is given: \to C = \frac{\to A \cdot \to B}{{| | B | |}^{2}} \to B$ $"the projection of "vec A " onto "vec B" is given: " vec C=(vec A*vec B)/||B||^2 vec B$
$\to C = - \frac{22}{{(\sqrt{82})}^{2}} (8 ˆ i - 3 ˆ j + 3 ˆ k)$ $vec C=-22/(sqrt82)^2(8 hat i-3 hat j+3 hat k)$
$\to C = - \frac{22}{82} (8 ˆ i - 3 ˆ j + 3 ˆ k)$ $vec C=-22/82(8 hat i-3 hat j+3 hat k)$
$\to C = - \frac{11}{41} (8 ˆ i - 3 ˆ j + 3 ˆ k)$ $vec C=-11/41(8 hat i-3 hat j+3 hat k)$

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What is the projection of $< - 5, 2, 8 >$ $<-5,2,8>$ onto $< 8, - 3, 3 >$ $<8,-3,3 >$ ?

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Explanation:

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What is the projection of <−5,2,8><-5,2,8> onto <8,−3,3><8,-3,3 >?

1 Answer

Explanation:

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What is the projection of $< - 5, 2, 8 >$ $<-5,2,8>$ onto $< 8, - 3, 3 >$ $<8,-3,3 >$ ?