Write a Vector in Terms of Its Magnitude and Direction
-$$| \mathbf { v } | = 10 , \theta = 120 ^ { \circ }$$
A) $\mathbf { v } = - 5 \mathbf { i } + 5 \sqrt { 3 } \mathbf { j }$
B) $\mathbf { v } = 5 \sqrt { 3 } \mathbf { i } - 5 \mathbf { j }$
C) $\mathbf { v } = - 5 \sqrt { 2 } \mathbf { i } + 5 \sqrt { 2 } \mathbf { j }$
D) $\mathbf { v } = 5 \mathbf { i } - 5 \sqrt { 3 } \mathbf { j }$

Question

Quizplus · Accepted Answer

A vector's components can be found using its magnitude and direction: $v_x = |v| \cos(\theta)$ and $v_y = |v| \sin(\theta)$. For $|v| = 10$ and $\theta = 120^\circ$, $v_x = 10 \cos(120^\circ) = -5$ and $v_y = 10 \sin(120^\circ) = 5\sqrt{3}$, making the vector $-5\mathbf{i} + 5\sqrt{3}\mathbf{j}$.

Write a Vector in Terms of Its Magnitude and Direction ∣v∣=10,θ=120∘| \mathbf { v } | = 10 , \theta = 120 ^ { \circ }∣v∣=10,θ=120∘

Write a Vector in Terms of Its Magnitude and Direction $| \mathbf { v } | = 10 , \theta = 120 ^ { \circ }$