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(a) (p + q)*(p + q) = p * p + 2p*q + q*q * means dot product. = 5^2 + 2(5)(7) cos 120 + 7^2 = 25 - 70 cos 60 + 49 = 74 - 35 = 39. so abs(p + q) = sqrt 39. (b) (q - r)*(q - r) = q*q - 2q*r + r*r = 7^2 - 2(7)(3)cos 60 + 3^2 = 49 - 21 + 9 = 37 so abs(q - r) = sqrt 37. (c) r = - 3p/5, so p - q + r = p - q - 3p/5 = 2p/5 - q so ( p - q + r)*(p - q + r) = (2p/5 - q)*(2p/5 - q) = (4/25)p*p - (4/5)p*q + q*q = (4/25)(25) - (4/5)(5)(7) cos 120 + 49 = 4 + 14 + 49 = 67 so abs(p - q + r) = sqrt 67.

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