Vector Addition and Subtraction Assignment

Vector Vector P Q has an initial point at (3, 3) and its terminal point is at (5, 7). Vector Vector R S has an initial point at (4, -6) and its terminal point is at (1, -5). What is the component form of vector ?PQ-RS

5,3

Given the four vectors in component form: a = 4i - 4j b = -5i + 8j c = -i - 3j d = 6i + 2j Choose the expression that produces the following resultant vectors. 6i + 9j = 2j = -8i + 13j = -10i - 7j =

6i + 9j = 2a + b - 3c 2j = d - 4a - 2b -8i + 13j = 5(a - c) + 3(b - d) -10i - 7j = c + 2(a - d) + b

Fumio performed the following operations on vectors u, v, and w, where u = ⟨6, -8⟩, v = ⟨1, 2⟩, w = ⟨3, -3⟩ 2u - 3(v + w) 2 ⟨6, -8⟩ - 3[⟨1, 2⟩ + ⟨3, -3⟩] ⟨12, -8⟩ - 3⟨4, -1⟩ ⟨12, -8⟩ + ⟨-12, 3⟩ ⟨0, -5⟩ What mistake did Fumio make?

A. He did not distribute the 2 to both components of vector u.

Given the following vectors in component form: r = ⟨2, 3⟩ s = ⟨5, -3⟩ t = ⟨-8, 6⟩ Check all expressions whose sum represents the same vector as (r + s) + t.

B. < 7, 0 > + < - 8, 6 > C. < 2, 3 > + < - 3, 3 > E. < - 6, 9 > + < 5, - 3 >

Consider the following vectors in polar form. |u| = 2 at ∠0° |v| = 4 at ∠45° What is the magnitude of vector w, if w = u - v?

B. |w| = 2.95

Which of the following shows a proper representation of vector addition using the head-to-tail method?

C.

Given the vectors in component form: r = ⟨8, 4⟩ s = ⟨-3, -4⟩ t = ⟨-5, 1⟩ Perform the operations. 5r - 3s + 8t What is the magnitude and direction angle of the resultant vector?

C. 41.0, θ = 77.3°

Consider the following vectors in component form a= <2,10> b=<-5,-14> c=a-b What is the magnitude and direction angle of vector c?

D. |c| = 25, θ = 73.7°

Let w represent the sum of vectors u and v. Find the magnitude of w and the angle between w and u given the following information: |u| = 14 |v| = 16 The angle between u and v is 60°. The magnitude of w is approximately _____. The angle between w and u is approximately _____°.

The magnitude of w is approximately 26. The angle between w and u is approximately 32.2°.

Given the following vectors in component form: u = ⟨10, 12⟩ v = ⟨- 3, y⟩ 5u = ⟨50, 60⟩ 5v = ⟨-15, 5y⟩ 5(u + v) = ⟨35, 40⟩ What is the y-component of vector v?

y = -4