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

1 Answer
Nov 22, 2016

Answer:

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

Explanation:

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〉#