Given the vector v lies in the yz-plane, has magnitude 8, and makes $\text { angle of } 150 ^ { \circ }$ with the positive y-axis. Find the component form of v.
A) $\mathbf { v } = \{ 0 , - 4 \sqrt { 3 } , \pm 4 \}$
B) $\mathbf { v } = ( 4 \sqrt { 3 } , 0,4 \}$
C) $\mathbf { v } = \{ 0 , - 4 \sqrt { 3 } , 4 \}$
D) $\mathbf { v } = \{ - 4 \sqrt { 3 } , 0 , \pm 4 \}$
E) $\mathbf { v } = \{ 0,4 \sqrt { 3 } , \pm 4 \}$

Question

Given the vector v lies in the yz-plane, has magnitude 8, and makes $\text { angle of } 150 ^ { \circ }$ with the positive y-axis. Find the component form of v. 
A) $\mathbf { v } = \{ 0 , - 4 \sqrt { 3 } , \pm 4 \}$
B) $\mathbf { v } = ( 4 \sqrt { 3 } , 0,4 \}$
C) $\mathbf { v } = \{ 0 , - 4 \sqrt { 3 } , 4 \}$
D) $\mathbf { v } = \{ - 4 \sqrt { 3 } , 0 , \pm 4 \}$
E) $\mathbf { v } = \{ 0,4 \sqrt { 3 } , \pm 4 \}$

Quizplus · Accepted Answer

The vector lies in the yz-plane, so its x-component is 0. The magnitude of the vector is 8, so its y-component is $8 \cos 150^\circ = -4\sqrt{3}$. The z-component is $8 \sin 150^\circ = 4$.

Given the Vector V Lies in the Yz-Plane, Has Magnitude angle of 150∘\text { angle of } 150 ^ { \circ } angle of 150∘

Given the Vector V Lies in the Yz-Plane, Has Magnitude $\text { angle of } 150 ^ { \circ }$