Four vectors all have the same magnitude.Vector 1 is at 60°,Vector 2 is at 135°,vector 3 is at 210°,and Vector 4 is at 315°.Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?

A) Vector 1,Vector 2
B) Vector 3,Vector 4
C) Vector 1,Vector 3
D) Vector 3,Vector 2
E) Vector 2,Vector 4

Question

Four vectors all have the same magnitude.Vector 1 is at 60°,Vector 2 is at 135°,vector 3 is at 210°,and Vector 4 is at 315°.Which vector has the greatest magnitude x-component and which vector has the greatest magnitude y-component?
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A) Vector 1,Vector 2
B) Vector 3,Vector 4
C) Vector 1,Vector 3
D) Vector 3,Vector 2
E) ​Vector 2,Vector 4

Quizplus · Accepted Answer

To find which vector has the greatest magnitude x-component, we need to look at the cosine values of each angle (cosine is the x-component of a vector with that angle). The cosine values are as follows:
Vector 1: cos(60°) = 0.5
Vector 2: cos(135°) = -0.707
Vector 3: cos(210°) = -0.5
Vector 4: cos(315°) = 0.707
Therefore, vectors 1 and 4 have the greatest magnitude x-components. 
To find which vector has the greatest magnitude y-component, we need to look at the sine values of each angle (sine is the y-component of a vector with that angle). The sine values are as follows:
Vector 1: sin(60°) = 0.866
Vector 2: sin(135°) = 0.707
Vector 3: sin(210°) = -0.866
Vector 4: sin(315°) = -0.707
Therefore, vectors 1 and 3 have the greatest magnitude y-components.
So the answer is C, Vector 1 and Vector 3.

Four Vectors All Have the Same Magnitude