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

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

Options:

  1. 13
  2. 12
  3. 5
  4. 17

Correct Answer: 13

Solution: 

Magnitude |C| = √(5^2 + (-12)^2) = √(25 + 144) = √169 = 13.

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

Practice Questions

Q1
What is the magnitude of the vector C = 5i - 12j?
  1. 13
  2. 12
  3. 5
  4. 17

Questions & Step-by-Step Solutions

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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