SOLUTION: Let CC and DD be points with position vectors c and d respectively. If |c|=5, |d|=7 and c⋅d=4, find vector|CD| How can i handle this problem? Thank you so much

Algebra ->  Vectors -> SOLUTION: Let CC and DD be points with position vectors c and d respectively. If |c|=5, |d|=7 and c⋅d=4, find vector|CD| How can i handle this problem? Thank you so much      Log On


   

Question 1041269: Let CC and DD be points with position vectors c and d respectively. If |c|=5, |d|=7 and c⋅d=4, find vector|CD|
How can i handle this problem?
Thank you so much
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let vector c = OC be (a,b) and let vector d = OD be (r,s)
==> vector CD is (r-a, s-b).
Now abs%28c%29%5E2+=+a%5E2%2Bb%5E2+=+25, and abs%28d%29%5E2+=+r%5E2%2Bs%5E2+=+49.
Also, c*d = 4 ==> ar + bs = 4 ==> 2ar + 2bs = 8
==> %28a%5E2%2Bb%5E2%29+-+%28+2ar+%2B+2bs%29+%2B+%28r%5E2%2Bs%5E2%29+
= %28a%5E2+-+2ar+%2B+r%5E2%29+%2B+%28b%5E2+-+2bs+%2B+s%5E2%29
=%28a-r%29%5E2+%2B+%28b-s%29%5E2+=+25+%2B+49+-+8+=+66.
But abs%28CD%29+=+sqrt%28%28a-r%29%5E2+%2B+%28b-s%29%5E2%29, and
therefore..
abs%28CD%29+=+sqrt%2866%29.