Vector = 1.00
+ -2.00
And vector
= 3)00
+ 4)00
What are the magnitude and direction of vector
=
+
?
A) 7.21 in a direction 33.7° counterclockwise from the positive x axis
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis

Question

Vector  = 1.00 
+ -2.00 
And vector 
= 3)00 
+ 4)00 
What are the magnitude and direction of vector 
= 
+ 
?
A) 7.21 in a direction 33.7° counterclockwise from the positive x axis 
B) 6.00 in a direction 63.4° counterclockwise from the positive x axis 
C) 4.47 in a direction 6.34° counterclockwise from the positive x axis 
D) 4.47 in a direction 26.6° counterclockwise from the positive x axis 
E) 7.21 in a direction 56.3° counterclockwise from the positive x axis

Quizplus · Accepted Answer

To find the magnitude and direction of the vector, we need to add the two given vectors and then use trigonometry.
Adding the two given vectors, we get: 
11ea8401_fb73_1bfe_aeff_69a4eefb1bbc_TB6682_11 + 11ea8401_fb73_1bff_aeff_817095d7c2a9_TB6682_11
= 11ea8401_fb73_1c00_aeff_4c56ed2b387a_TB6682_11
Now, we can find the magnitude using the Pythagorean theorem:
magnitude = sqrt((1.00)^2 + (-2.00)^2 + (3.00)^2 + (4.00)^2) = 4.47
To find the direction, we can use trigonometry. The angle that the vector makes with the positive x-axis is given by:
angle = atan2(sum of y-components, sum of x-components)
angle = atan2(3.00 + 4.00, 1.00 - 2.00) = atan2(7.00, -1.00)
However, since the angle is counterclockwise from the positive x-axis, we need to add 360° to get the angle in the standard range of 0-360°:
angle = atan2(7.00, -1.00) + 360° = 286.6°
Finally, we can subtract the angle from 360° and convert to radians to get the counterclockwise direction from the positive x-axis:
direction = (360° - 286.6°) * pi/180° = 26.6°
Therefore, the magnitude and direction of the vector are 4.47 in a direction 26.6° counterclockwise from the positive x-axis, which corresponds to choice D.