What is the projection of $(2i -3j + 4k)$ onto $(- 5 i + 4 j - 5 k)$ ?

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Answer 1 · 2017-01-02T15:04:34

The answer is $=-7/11〈-5,4,-5〉$

The vector projection of $vecb$ onto $veca$ is

$=(veca.vecb)/(∣veca∣)^2veca$

The dot product is

$veca.vecb=〈2,-3,4〉.〈-5,4,-5〉=(-10-12-20)=-42$

The modulus of $veca$ is $=∣〈-5,4,-5〉∣$

$=sqrt(25+16+25)=sqrt66$

The vector projection is $=-42/66〈-5,4,-5〉$

$=-7/11〈-5,4,-5〉$

What is the projection of (2i -3j + 4k) (2i -3j + 4k) onto (- 5 i + 4 j - 5 k)(- 5 i + 4 j - 5 k)?