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Given the vector F = 18N, \theta = 83 degrees, find the magnitude and direction of the opposite...

Question:

Given the vector F = 18N, {eq}\theta {/eq} = 83 degrees, find the magnitude and direction of the opposite vector F.

Resolution of Vectors:

Let the vector {eq}\vec A {/eq} is directed at an angle {eq}\theta {/eq} from the x-axis. Then we can write the vector as a sum of its components along the x- axis and the y-axis as in the following expression:

  • {eq}\vec A = (|\vec A| \cos \theta) \hat i +(|\vec A| \sin \theta )\hat j {/eq}

where:

  • {eq}|\vec A| {/eq} is the magnitude of the vector.

Answer and Explanation:

Given:

  • The force vector is F = 18 N, it make an angle {eq}\theta = 83^o {/eq} from the +X axis.

The opposite vector will have same magnitude ie F' = 18 N.

The angle of the opposite vector is {eq}\theta ' = (180+83)^o = 263^o {/eq} from the +X axis.


Learn more about this topic:

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Vectors: Definition, Types & Examples

from Common Entrance Test (CET): Study Guide & Syllabus

Chapter 57 / Lesson 3
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