Dot Product and Work Assignment

Given the vectors u and v. What is u · v? 19 59 61 160

A. 19

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. 18 Joules 54 Joules 60 Joules 78 Joules

B. 54 Joules

Which sets of vectors are orthogonal? Check all that apply. a = 〈-1, 0〉 and b = 〈1, 0〉 c = 〈1, 0〉 and d = 〈0, -1〉 e = 〈-4, -6〉 and f = 〈12, 8〉 g = 〈4, -6〉 and h = 〈12, 8〉 v = 〈10, -5〉 and w = 〈-10, -20〉 x = 〈10, -5〉 and y = 〈-10, -2〉

B. c = 〈1, 0〉 and d = 〈0, -1〉 D. g = 〈4, -6〉 and h = 〈12, 8〉 E. v = 〈10, -5〉 and w = 〈-10, -20〉

Find the dot product of vectors u and v, where |u| = 12, |v| = 7, and the angle between is θ = 55°. u · v = 68.81 u · v = 48.18 u · v = 10.90 u · v = 2.87

B. u · v = 48.18

Find the angle θ between u = 〈6, -5〉 and v = 〈11, 8〉. θ = 3.77° θ = 75.83° θ = 89.87° θ = 165.83°

B. θ = 75.83°

A boat is being towed such that the tow line is at an angle of 30° with respect to the surface of the ocean. If the boat is towed with a force of 50 Newtons for 7,000 meters, approximately how much work is done? 152,000 Joules 175,000 Joules 303,000 Joules 350,000 Joules

C. 303,000 Joules

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.

C. 49/4 B. 539

Two vectors of lengths 4 and 6 have a dot product equal to 24. Which is true about the vectors? They form an acute angle. They form an obtuse angle. They point in the same direction. They point in opposite directions.

C. They point in the same direction.

Find the dot product of u = 〈3, -4〉 and v = 〈-7, -2〉. u · v = -29 u · v = -22 u · v = -13 u · v = -10

C. u · v = -13

Find the angle θ between vectors r and s, where |r| = 16, |s| = 9, and r · s = 125. θ = 85.87° θ = 82.65° θ = 29.77° θ = 16.26°

C. θ = 29.77°