High School

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You have two vectors, A and B, such that A has a magnitude of 35.5 and B has a magnitude of 56.6. What is the magnitude (in cm) of the vector C?

A. 35.5
B. 56.6
C. 91.1
D. 21.1

Answer :

Final answer:

The magnitude of vector C is 91.1 cm. (option c).

Explanation:

To find the magnitude of vector C, we can use the triangle law of vector addition. According to this law, the magnitude of the resultant vector formed by adding two vectors is equal to the square root of the sum of the squares of the magnitudes of the individual vectors.

Mathematically, we represent this as:

C = √(A^2 + B^2)

Given that vector A has a magnitude of 35.5 cm and vector B has a magnitude of 56.6 cm, we can substitute these values into the equation:

C = √(35.5^2 + 56.6^2)

C = √(1260.25 + 3201.76)

C = √4462.01

C ≈ 91.1 cm

Therefore, the magnitude of vector C is approximately 91.1 cm, which corresponds to option c) in the question. This calculation follows the principles of vector addition and Pythagoras' theorem to determine the resultant magnitude. (option c).

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