Vector Components Worksheet
A Grade 11 Math worksheet covering vector components, resolution of vectors, and calculations involving magnitude and direction.
Includes
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Vector Components Worksheet
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Date:
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Read each question carefully and provide your answer in the space provided. Show all your work for full credit.
1. Resolve the vector with magnitude 10 units and direction 30° from the positive x-axis into its horizontal (x) and vertical (y) components. Show your calculations.
x-component:
y-component:
2. A force of 50 N acts at an angle of 60° above the horizontal. Calculate the horizontal and vertical components of this force.
3. The horizontal component of a vector is calculated using the function, while the vertical component uses the function.
4. To find the magnitude of a vector from its components, we use the theorem.
5. The direction of a vector can be found using the inverse function of its components.
6. A vector has an x-component of 3 and a y-component of 4. What is its magnitude?
5
7
1
12
7. If a vector's x-component is 0 and its y-component is negative, in which direction does the vector point?
Positive x-axis
Negative x-axis
Positive y-axis
Negative y-axis
8. Vector A has components (3, 5). Vector B has components (-2, 6). Find the components of the resultant vector R = A + B.
9. A boat travels 15 km East and then 20 km North. What is the magnitude and direction of the boat's displacement from its starting point?
10. The components of a vector are always positive.
True
False
11. If a vector lies entirely on the y-axis, its x-component is zero.
True
False
12. Plot the vector with components (4, -3) on the coordinate plane below. Label the x and y components.