Find the magnitude and direction angle (to the nearest tenth) for each vector. Give the measure of the direction angle as
an angle in [0,360°].
-$\langle 10,10 \rangle$
A) $10 \sqrt { 2 } ; 45 ^ { \circ }$
B) $20 ; 45 ^ { \circ }$
C) $10 ; 225 ^ { \circ }$
D) $10 \sqrt { 2 } ; 225 ^ { \circ }$

Question

Quizplus · Accepted Answer

The magnitude of the vector $\langle 10,10 \rangle$ is calculated using the formula $\sqrt{x^2 + y^2}$, which gives $\sqrt{10^2 + 10^2} = \sqrt{200} = 10\sqrt{2}$. The direction angle, measured from the positive x-axis, is found using $\tan^{-1}(y/x)$, which gives $\tan^{-1}(10/10) = \tan^{-1}(1) = 45^\circ$, placing the vector in the first quadrant.

Find the Magnitude and Direction Angle (To the Nearest Tenth) ⟨10,10⟩\langle 10,10 \rangle⟨10,10⟩

Find the Magnitude and Direction Angle (To the Nearest Tenth) $\langle 10,10 \rangle$