What is the projection of #<3,-7,4># onto #<1,4,0 >#?

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Answer 1 · 2016-11-22T07:37:58

The projection is #〈-25/17,-100/17,0〉#

Let #vecb=〈3,-7,4〉# and #veca=〈1,4,0〉#

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

#(veca.vecb)/(∥veca∥^2)veca#

The dot product is #veca.vecb#

#=〈3,-7,4〉.〈1,4,0〉=3*1-7*4+0=-25#

The modulus of #veca=∥1,4,0∥=sqrt(1+16)=sqrt17#

So the vector proection is

#=-25/17〈1,4,0〉=〈-25/17,-100/17,0〉#