1.5 Vector resolution
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The process of breaking a vector into its components is called resolving into components
Graphical method of vector resolution
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In the rectangular coordinate system shown in Figure
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Vector A is broken up or resolved into two component vectors.
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One, Ax , is parallel to the x-axis, and the other, Ay , is parallel to the y-axis.
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The components are calculated according to these equations, where the angle is measured counterclockwise from the positive x-axis.
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You can see that the original vector is the sum of the two component vectors.
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Ax and Ay are at a right angle (900), the magnitude of the resultant vector can be calculated using the Pythagorean Theorem.
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To find the angle or direction of the resultant, recall that the tangent of the angle that the vector makes with the x-axis is given by the following.
- A motorist undergoes a displacement of 250 km in a direction 30⁰ North of East. Resolve this displacement into its components.
A boy walks 3 km due East and then 2 km due North. What is the magnitude and direction of his displacement vector?
- What is resolution of a vector?
2. Draw simple vector diagrams and resolve them into their components.
3. A car travels 10 km due North and then 5 km due West. Find graphically and analytically the magnitude and direction of the car’s resultant vector.
4. A girl walks 25.0o North of East for 3.10 km. How far would she have to walk due North and due East to arrive at the same location?
