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Questions and Answers
What is the result of adding two vectors A = 3i + 4j and B = 2i - 5j?
If vector A = 2i + 3j and vector B = 4i - 2j, what is the result of A - B?
What is the magnitude of the vector A = 3i + 4j?
If two vectors have the same direction, what can be said about their addition?
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What is true about the subtraction of two vectors with the same direction?
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Study Notes
Vector Addition and Subtraction
- The result of adding two vectors A = 3i + 4j and B = 2i - 5j is (3i + 4j) + (2i - 5j) = (3 + 2)i + (4 - 5)j = 5i - j.
Vector Subtraction
- The result of subtracting vector B = 4i - 2j from vector A = 2i + 3j is (2i + 3j) - (4i - 2j) = (2 - 4)i + (3 + 2)j = -2i + 5j.
Vector Magnitude
- The magnitude of the vector A = 3i + 4j is √(3² + 4²) = √(9 + 16) = √25.
Vector Directions
- If two vectors have the same direction, their addition results in a vector with the same direction, but with a magnitude equal to the sum of the magnitudes of the individual vectors.
- If two vectors have the same direction, their subtraction results in a vector with the same direction, but with a magnitude equal to the difference of the magnitudes of the individual vectors.
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Description
This quiz covers the basics of vector operations, including adding and subtracting vectors, and calculating their magnitude. It also explores the properties of vectors with the same direction.
