# Vectors Exam1 and Problem Solutions

1. Find A+B+C. First, we find A+B then add it to vector C. We find R₁, now we add C to R₁ to find resultant vector. R₂=A+B+C

2. Find resultant vector. Since; A+B=E and C+D=E

R=A+B+C+D+E

R=E+E+E=3E

3. A and A+2B vectors are given below. Find vector B We use vector addition properties. A+2B-A=2B To get vector B, we multiply 2B with 1/2.

4. Find resultant vector. F₁+F₂=5-2=3N F₁+F₂+F₃=R=3N

5. Which one of the following statements is true? I. A=B in magnitude

II. A=2C

III. E=2D

IV. A=B

As you can see in the figure given above, A and B are equal in magnitude, so I. is true.

If you multiply C with 2, you get A, this means that II. is also true

E =2D in magnitude but not in direction. Thus; III. is false.

A = B in magnitude but they have different directions, thus; IV is also false.

6. If α₃<α₂<α₁ and R₁=R₂=R₃, find the relation between F₁, F₂ and F₃. Decreasing in the angle between forces increases the resultant force.

If α₁=α₂, then R₁>R₂ and F₂>F₃

If α₂=α₃, then R₂>R₃ and F₁>F₂

F₁>F₂>F₃

7. Resultant vector of K, L and M is zero. Which one of the following statements given below is definitely false?

I. Ky and Ly components are equal vectors

II. K+L=M

III. α=60⁰ I. Ky=-Ly, they are equal in magnitude but opposite in directions, thus they are not equal vectors.I. is false.

II. Magnitude of K+L=M, but directions are opposite, thus II is also wrong.

III: α=60⁰ is possible. III is not exactly false.