Grade 12 Vector Components Worksheet

Grade 12 Vector Components Worksheet

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?

7. If a vector has components (3, -4), what is its magnitude?

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 \(\vec{R} = \vec{A} + \vec{B}\).