Vector A has a magnitude of 3.0 units and makes an angle of $-90.0^{\circ}$ with the positive x-axis.Vector B has a magnitude of 4.0 units and makes an angle of $-120^{\circ}$ with the positive x-axis.What is the magnitude of the vector sum of A + B?
A) 1.0 units
B) 6.8 units
C) 4.0 units
D) -6.8 units

Question

Quizplus · Accepted Answer

To find the vector sum of A + B, we need to first add the x-components and y-components of each vector. Using trigonometry, we can find that the x-component of vector A is 0 and the y-component is -3. The x-component of vector B is -2.0 units and the y-component is -3.5 units. 
Therefore, the sum of the x-components is 0 + (-2.0) = -2.0 units, and the sum of the y-components is -3 + (-3.5) = -6.5 units. 
Using the Pythagorean theorem, we can find the magnitude of the vector sum:
|A + B| = sqrt((-2.0)^2 + (-6.5)^2) = 6.8 units
Therefore, the answer is B.

Vector a Has a Magnitude of 3 −90.0∘-90.0^{\circ}−90.0∘ With the Positive X-Axis

Vector a Has a Magnitude of 3 $-90.0^{\circ}$ With the Positive X-Axis