What is the projection of #< -3, 6, 7># onto #< 5, 1, -5>#?

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Answer 1 · 2016-12-01T15:16:08

The answer is #=-44/51〈5,1,-5〉#

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

#=(veca.vecb)/(∥veca∥)*veca#

Here, #veca=〈5,1,-5〉#

#vecb=〈-3,6,7〉#

The dot product is

#veca.vecb=〈5,1,-5〉.〈-3,6,7〉=-15+6-35=-44#

The modulus of #veca=∥veca∥=∥〈5,1,-5〉∥#

#=sqrt(25+1+25)=sqrt51#

So, the projection is #=-44/51〈5,1,-5〉#