Dot Product and Work

Question 1

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

Revolt · Accepted Answer

C: u · v = –13

Question 2

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

Revolt · Accepted Answer

B: θ = 75.83°

Question 3

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〉

Revolt · Accepted Answer

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

Question 4

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.

Revolt · Accepted Answer

B: 54 Joules

Question 5

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

Revolt · Accepted Answer

B: u · v = 48.18

Question 6

What is u · v?

Revolt · Accepted Answer

A: 19

Question 7

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

Revolt · Accepted Answer

C: θ = 29.77°

Question 8

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 =

Revolt · Accepted Answer

C: ✔ 49/4

Question 9

Two vectors of lengths 4 and 6 have a dot product equal to 24. Which is true about the vectors?

Revolt · Accepted Answer

C: They point in the same direction.

Question 10

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

Revolt · Accepted Answer

C: 303,000 Joules

Dot Product and Work Answers

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