High School

The three vectors in Fig. 3-31 have magnitudes [tex]a = 3.00 \, \text{m}[/tex], [tex]b = 4.00 \, \text{m}[/tex], and [tex]c = 10.0 \, \text{m}[/tex]. What are:

(a) The x-component?
(b) The y-component?

A. (a) 3.00 m, (b) 4.00 m
B. (a) 4.00 m, (b) 3.00 m
C. (a) 6.00 m, (b) 8.00 m
D. (a) 8.00 m, (b) 6.00 m

Answer :

Final answer:

The x-component and y-component of the given vectors cannot be determined without the angles.

Explanation:

To find the x-component and y-component of a vector, we can use the trigonometric relationships. In this case, we have three vectors with magnitudes a = 3.00m, b = 4.00m, and c = 10.0m.

For vector a, the x-component (Ax) can be found using the formula Ax = a * cos(θ), where θ is the angle the vector makes with the x-axis. Since the angle is not given, we cannot determine the x-component.

For vector b, the x-component (Bx) can be found using the formula Bx = b * cos(θ), where θ is the angle the vector makes with the x-axis. Since the angle is not given, we cannot determine the x-component.

For vector c, the x-component (Cx) can be found using the formula Cx = c * cos(θ), where θ is the angle the vector makes with the x-axis. Since the angle is not given, we cannot determine the x-component.

Therefore, the answer is (a) and (b) cannot be determined.

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