SOLUTION: Find two vector v1 and v2 whose sum is <4,1>, where v1 is parallel to <3,5> while v2 is to <3,5>

Algebra ->  Vectors -> SOLUTION: Find two vector v1 and v2 whose sum is <4,1>, where v1 is parallel to <3,5> while v2 is to <3,5>      Log On


   

Question 1147491: Find two vector v1 and v2 whose sum is <4,1>, where v1 is parallel to <3,5> while v2 is to <3,5>
Answer by greenestamps(13209) About Me  (Show Source):
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A vector parallel to <3,5> is of the form <3a,5a>.

A vector perpendicular to <3,5> is of the form <5b,-3b>. (The dot product has to be 0.)

We want <3a,5a> + <5b,-3b> to be equal to <4,1>.

3a%2B5b+=+4
5a-3b+=+1

9a%2B15b+=+12
25a-15b+=+5
34a+=+17
a+=+1%2F2
b+=+1%2F2

ANSWER: v1 = <3/2,5/2>; v2 = <5/2,-3/2> --> v1+v2 = <8/2,2/2> = <4,1>