Additional Concepts
-$$\mathbf { v } = - 12 \mathbf { i } + 5 \mathbf { j }$$
A) $13 ; 157.4 ^ { \circ }$
B) $13 ; 22.6 ^ { \circ }$
C) $15 ; 157.4 ^ { \circ }$
D) $13 ; 112.6 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the vector $\mathbf{v} = -12\mathbf{i} + 5\mathbf{j}$ is calculated using the formula $\sqrt{(-12)^2 + 5^2} = 13$. The direction angle $\theta$ with the positive x-axis can be found using $\tan^{-1}\left(\frac{5}{-12}\right)$, which gives an angle in the fourth quadrant. To find the angle in standard position (measured counterclockwise from the positive x-axis), we add $180^\circ$ to the calculated angle, resulting in $157.4^\circ$.

Additional Concepts - v=−12i+5j\mathbf { v } = - 12 \mathbf { i } + 5 \mathbf { j }v=−12i+5j

Additional Concepts
- $\mathbf { v } = - 12 \mathbf { i } + 5 \mathbf { j }$