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〉#