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What is the magnitude of the vector v = (3, -4)?
What is the magnitude of the vector v = (3, -4)?
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Q1
What is the magnitude of the vector v = (3, -4)?
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Magnitude of v = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Questions & Step-by-step Solutions
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Q
Q: What is the magnitude of the vector v = (3, -4)?
Solution:
Magnitude of v = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.
Steps: 8
Show Steps
Step 1: Identify the components of the vector v. Here, v = (3, -4), so the components are 3 and -4.
Step 2: Use the formula for the magnitude of a vector, which is √(x^2 + y^2), where x and y are the components of the vector.
Step 3: Substitute the values of the components into the formula. This gives us √(3^2 + (-4)^2).
Step 4: Calculate 3^2, which is 9.
Step 5: Calculate (-4)^2, which is 16.
Step 6: Add the results from Step 4 and Step 5. So, 9 + 16 = 25.
Step 7: Take the square root of 25. This gives us √25 = 5.
Step 8: Conclude that the magnitude of the vector v is 5.
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