What is the projection of #(2i + 3j – 7k)# onto # (3i – 4j + 4k)#?

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Answer 1 · 2016-12-20T09:38:36

The answer is #=34/41〈3,-4,4〉#

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

#=(veca.vecb)/(∥veca∥^2)veca#

The dot product is #veca.vecb=〈2,3,-7〉.〈3,-4,4〉#

#=(6-12-28)=34#

The modulus of #veca# is #=∥veca∥=∥〈3,-4,4〉∥#

#=sqrt(9+16+16)=sqrt41#

The vector projection is #=34/41〈3,-4,4〉#