Grade 12 Vector Components Worksheet
This worksheet covers vector components, including resolving vectors, finding magnitudes, and unit vectors, suitable for Grade 12 math students.
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Grade 12 Vector Components Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. A force of 150 N is applied at an angle of 30° to the horizontal. Resolve this force into its horizontal and vertical components.
2. A vector has an x-component of 20 m/s and a y-component of 15 m/s. Calculate the magnitude and direction (angle with the positive x-axis) of the resultant vector.
3. The process of breaking a vector into its horizontal and vertical parts is called .
4. The magnitude of a vector can be found using the theorem if its components are known.
5. A vector with a magnitude of 1 is called a vector.
6. A projectile is launched with an initial velocity of 50 m/s at an angle of 60° above the horizontal. What is its initial vertical component of velocity?
25 m/s
43.3 m/s
50 m/s
86.6 m/s
7. If a vector has components (3, -4), what is its magnitude?
1
5
7
25
8. Find the unit vector in the same direction as vector \(\vec{v} = \begin{pmatrix} 6 \\ -8 \end{pmatrix}\).
9. Given two vectors \(\vec{A} = 3\hat{i} + 4\hat{j}\) and \(\vec{B} = -2\hat{i} + 5\hat{j}\), find the components of the resultant vector \(\vec{R} = \vec{A} + \vec{B}\).