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