Vector
Has a magnitude of 8.0 m and points east,vector
Has a magnitude of 6.0 m and points north,and vector
Has a magnitude of 5.0 m and points west.The resultant vector
+
+
Is given by
A)2.0 m at an angle 63° north of east.
B)2.0 m at an angle 63° east of north.
C)6.7 m at an angle 63° east of north.
D)6.7 m at an angle 63° north of east.
E)3.8 m at an angle 67° north of east.

Question

Vector 
Has a magnitude of 8.0 m and points east,vector 
Has a magnitude of 6.0 m and points north,and vector 
Has a magnitude of 5.0 m and points west.The resultant vector 
+ 
+ 
Is given by
A)2.0 m at an angle 63° north of east. 
B)2.0 m at an angle 63° east of north. 
C)6.7 m at an angle 63° east of north. 
D)6.7 m at an angle 63° north of east. 
E)3.8 m at an angle 67° north of east.

Quizplus · Accepted Answer

To find the resultant vector, we can use the Pythagorean theorem to find the magnitude, and then use trigonometry to find the angle.

Magnitude: 
R = sqrt((8.0)^2 + (6.0)^2 + (5.0)^2) 
R = 10.78 m

Angle: 
Using trigonometry, we have: 
tan(theta) = opposite/adjacent = (sum of all north-pointing components) / (sum of all east-pointing components)

tan(theta) = (6.0) / (8.0 + (-5.0)) = 0.75

theta = tan^-1(0.75) = 36.87°

The question is asking for the angle north of east, so we subtract 36.87° from 90°: 
90° - 36.87° = 53.13°

Therefore, the answer is D) 6.7 m at an angle 63° north of east.

Vector Has a Magnitude of 8.0 M and Points East,vector