Find the component form of v given its magnitude and the angle it makes with the positive x-axis. ?
Magnitude
Angle $\| \mathbf { v } \| = 6$ $45 ^ { \circ }$ ?
A)? $\langle - 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$
B)? $\langle - 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$
C)? $\langle 3,3 \rangle$
D)? $\langle 3 \sqrt { 2 } , 3 \sqrt { 2 } \rangle$
E)? $\langle 3 \sqrt { 2 } , - 3 \sqrt { 2 } \rangle$

Question

Quizplus · Accepted Answer

The component form of a vector given its magnitude and angle can be found using the formulas $v_x = \|v\| \cos(\theta)$ and $v_y = \|v\| \sin(\theta)$. For a magnitude of 6 and an angle of 45 degrees, both components are $6 \cos(45^\circ) = 6 \sin(45^\circ) = 3\sqrt{2}$, resulting in the vector $\langle 3\sqrt{2}, 3\sqrt{2} \rangle$.

Find the Component Form of V Given Its Magnitude and the Angle