Dot Product and Work Answers

Find the dot product of u = 〈3, –4〉 and v = 〈–7, –2〉.

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Find the angle θ between u = 〈6, –5〉 and v = 〈11, 8〉.

Find the dot product of vectors u and v, where |u| = 12, |v| = 7, and the angle between is θ = 55°.

Find the angle θ between vectors r and s, where |r| = 16, |s| = 9, and r · s = 125.

Given the vectors a and b, with lengths 21 and 44 respectively, and cosine of the angle between them equal to , find the scalar projection of a onto b and a · b. ab = a · b =

Find the work done by a force that is given by the vector ⟨2, 6⟩ in moving an object in a straight line from point R(–3, 2) to point S(9, 7). Assume that the units in the coordinate plane are meters.

If the boat is towed with a force of 50 Newtons for 7,000 meters, approximately how much work is done?