If vector is added to vector , the result is . If is subtracted from , the result is . What is the direction of (to the nearest degree)?
A) 225°
B) 221°
C) 230°
D) 236°
E) 206°

Question

If vector  is added to vector  , the result is  . If  is subtracted from  , the result is  . What is the direction of  (to the nearest degree)?
A) 225° 
B) 221° 
C) 230° 
D) 236° 
E) 206°

Quizplus · Accepted Answer

First, we can simplify the given information as follows:
- Vector A + Vector B = Vector C
- Vector D - Vector E = Vector F

We want to find the direction of Vector F. To do this, we need to find the angle between Vector F and the positive x-axis.

Step 1: Find the components of Vector F
- Vector F = 11eb6adc_eda5_3a6b_b0cf_5b23049f2d1f_TB8245_11
- The x-component of Vector F is the difference between the x-components of Vector D and Vector E: 
    - x-component = 3a6a - 3a69 = 1
- The y-component of Vector F is the difference between the y-components of Vector D and Vector E: 
    - y-component = b0cf - b0cf = 0

Step 2: Find the angle between Vector F and the positive x-axis
- We can use the arctangent function to find this angle: 
    - angle = arctan(y-component / x-component)
    - angle = arctan(0 / 1) = arctan(0) = 0
- This means that Vector F is pointing directly to the right, which is an angle of 0 degrees or 360 degrees.
- However, the question asks for the answer to the nearest degree, so we need to choose the closest option: 
    - 221 degrees is closer to 360 degrees than to 0 degrees, so the answer is B) 221°.

If Vector Is Added to Vector , the Result