Answer :
Component of b on a .9622 projection of b on a = 25/root(27),-1/root(27),1/root(27)
A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.
vector a = (5,-1,1)
vector b = (-2,-3,2)
Scalar projection of b onto a
comp of b on a = a.b/ |a|
a.b = 5*-2+-1*-3 + 1*2 = 5
|a| = [tex]\sqrt{5^{2}+-1^{2}+1^{2} }[/tex]
|a| = [tex]\sqrt{27}[/tex]
component of b on a = a.b/|a|
= 5/[tex]\sqrt{27}[/tex]
=.9622
Vector projection of b onto a
projection of b on a =( a.b/[tex](|a|)^){2}[/tex]).a
a.b/|a| = .9622
( a.b/[tex](|a|)^){2}[/tex]).a = 5/[tex]\sqrt{27}[/tex](5,-1,1)
projection of b on a = 25/root(27),-1/root(27),1/root(27)
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