There are 3 vectors:
p= 7i + 10j
q= 3i + 12j
r= -i +4j

Could you show me how to find the angle PQR. using the scalar product.

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  1. I will associate your vectors to have endpoints
    P(7,10), Q(3,12) and R(-1,4)
    then vector(PQ) = (-4,2)
    vector(QR) = (-4,-8)

    then PQ.QR = |PQ||QR|cos(theta), where theta is the angle between them
    16-16 = |PQ||QR|cos(theta)
    cos(theta) = 0
    theta = 90 degrees

    (notice the slope of lines PQ and QR are negative reciprocals of each other, so PQ and QR are perpendicular)

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