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A. Calculate the scalar projection of (3,5) onto (7,-2). B. Compute v1+v2, v1-v2, and v2-v1.

 May 17, 2016
edited by Guest  May 17, 2016
 #1
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I'm not sure what is meant by "scalar" projection, but, calling  V1 = (3,5)   and V2  = ( 7, -2), the projection of   V1 onto V2 is given by :

 

proj V2  V1  =    [V1 * V2] * [ V2 ]

                        ------------

                         ll  V2  ll 2

 

V1 * V2   = [3 *7 + 5 (-2)] =  [21 - 10  ]  =   11

 

ll V2 ll 2  =  72 + (-2)2  = 49 + 4   = 53

 

So

 

proj V2  V1  =    [11] * [ V2 ]       =   < 77/53 , -22/53  >

                        -------

                         [53]

 

 

2) V1 + V2   =  < 3 + 7 , 5 +  - 2 >   =  < 10, 3  >

 

3) V1 - V2  = < 3 - 7, 5 - (-2) >   =  < -4, 7  >

 

4) V2 - V1  =  < 7 - 3, -2 - 5>   = < 4,  -7  >

 

 

 

cool cool cool

 May 17, 2016

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