Vector 1 is 7 units long and is at 70°.Vector 2 is 5 units long and is at 155°.Vector 3 is 3 units long and is at 225°.Which vector has equal-magnitude components?
A)Vector 1
B)Vector 2
C)Vector 3
D)None of the vectors has equal-magnitude components.

Question

Quizplus · Accepted Answer

To determine if a vector has equal-magnitude components, we need to see if its horizontal and vertical components are equal.

The horizontal component of Vector 1 is 7*cos(70°) ≈ 2.2799. 
The vertical component of Vector 1 is 7*sin(70°) ≈ 6.5792. 
So, the components are not equal.

The horizontal component of Vector 2 is 5*cos(155°) ≈ -1.9533. 
The vertical component of Vector 2 is 5*sin(155°) ≈ 4.6712. 
So, the components are not equal.

The horizontal component of Vector 3 is 3*cos(225°) ≈ -2.1213. 
The vertical component of Vector 3 is 3*sin(225°) ≈ -2.1213. 
So, the components are equal.

Therefore, the answer is choice C, Vector 3.

Vector 1 Is 7 Units Long and Is at 70°