Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 30°.
A) $\langle 4 \sqrt { 3 } , 4 \rangle$
B) $\langle 4,4 \sqrt { 3 } \rangle$
C) $\langle 8,8 \sqrt { 3 } \rangle$
D) $\langle 8 \sqrt { 3 } , 8 \rangle$
E) $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Question

Find the component form of v if $\| \mathbf { v } \| = 8$ and the angle it makes with the x-axis is 30°.
A)  $\langle 4 \sqrt { 3 } , 4 \rangle$
B)  $\langle 4,4 \sqrt { 3 } \rangle$
C)  $\langle 8,8 \sqrt { 3 } \rangle$
D)  $\langle 8 \sqrt { 3 } , 8 \rangle$
E)  $\langle 4 \sqrt { 2 } , 4 \sqrt { 2 } \rangle$

Quizplus · Accepted Answer

The component form of a vector can be found using the magnitude and direction angle: $v_x = \| \mathbf { v } \| \cos(\theta)$ and $v_y = \| \mathbf { v } \| \sin(\theta)$. For $\| \mathbf { v } \| = 8$ and $\theta = 30°$, $v_x = 8 \cos(30°) = 8 \times \frac{\sqrt{3}}{2} = 4\sqrt{3}$ and $v_y = 8 \sin(30°) = 8 \times \frac{1}{2} = 4$, making the component form $\langle 4 \sqrt { 3 } , 4 \rangle$.

Find the Component Form of V If ∥v∥=8\| \mathbf { v } \| = 8∥v∥=8

Find the Component Form of V If $\| \mathbf { v } \| = 8$