What is the magnitude of the vector C = 5i - 12j?

What is the magnitude of the vector C = 5i - 12j?

Step 1: Identify the components of the vector C. Here, C = 5i - 12j means the x-component is 5 and the y-component is -12.
Step 2: Write down the formula for the magnitude of a vector. The formula is |C| = √(x^2 + y^2), where x and y are the components.
Step 3: Substitute the values of the components into the formula. So, |C| = √(5^2 + (-12)^2).
Step 4: Calculate 5^2, which is 25.
Step 5: Calculate (-12)^2, which is 144.
Step 6: Add the results from Step 4 and Step 5. So, 25 + 144 = 169.
Step 7: Take the square root of 169. √169 = 13.
Step 8: Conclude that the magnitude of the vector C is 13.

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