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

Question

1551 views around the world

You can reuse this answer
Creative Commons License

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 $=-44/51〈5,1,-5〉$

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