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## Vector Exam1 and Problem Solutions

**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.

**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=60^{0}

**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=60^{0} is possible.III is not exactly false.

Author: Mrs. Şerife (Erden) SARICA

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