SOLUTION: Calculate proj v to u. u=<2,9> and v= (-3,4) Resolve u into u1 and u2, where u1 is parallel to v and u2 is orthogonal to v.

Question 1042853: Calculate proj v to u. u=<2,9> and v= (-3,4)
Resolve u into u1 and u2, where u1 is parallel to v and u2 is orthogonal to v.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
The projection of v onto u is given by
.
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First find vector , which is the component of vector u along vector v.
This is given by . This is .
Now let's find . A vector orthogonal (perpendicular) to v = <-3,4> is = <4,3>, since their dot product is -3*4 + 4*3 = 0.
Next find the component of u along .
It is given by
.
This is .
Since it is easy to verify that , we have found the resolution of u into its orthogonal components.
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