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Interpret this projection graphically. I calculated the Scalar projection of (5,3) and...

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atrinity | (Level 1) Honors

Posted May 14, 2013 at 7:43 PM via web

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Interpret this projection graphically.

I calculated the Scalar projection of (5,3) and (7,-2) to be 3.57, now the only issue I am having is interpreting this graphically.

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 14, 2013 at 8:43 PM (Answer #1)

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The scalar projection of one vector onto the other is simply determining what part of the vector being projected on is in the "shadow" of the projected vector.

First, as you have calculated, you have to determine the magnitude of the projection:

Let `theta` = the angle between vector A (5,3) and vector B (7,-2)
Let `A_B` = the magnitude of the projection of vector A onto vector B

`costheta=(A*B)/(|A||B|)`

`A_B=|A|costheta=(|A|A*B)/(|A||B|)=(A*B)/|B|`

`A*B=(5)(7)+(3)(-2)=29`

`|B|=sqrt(7^2+(-2)^2)=7.28`

`A_B=29/7.28=3.98`

The graphical representation is below.  The red part of the line is the scalar projection of A onto B.

Sources:

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