Questions and Answers
What is the ordered pair representing YZ if Y(14,-23) and Z(23,-14)? Then find the magnitude of YZ.
(9,9); 9sqrt2
What is the ordered pair representing YZ if Y(4,2) and Z(2,8)? Then find the magnitude of YZ.
(-2,6); 2sqrt10
What is the ordered pair that represents the vector from A(31,-33) to B(36,-45)? Then find the magnitude of AB.
(5,-12); 13
Find the magnitude of the vector from the origin to (-7,-5) and write the vector as the sum of unit vectors.
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What is the ordered pair representing YZ if Y(-2,5) and Z(1,3)? Then find the magnitude of YZ.
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Identify the ordered pair that represents the vector from A(-9,9) to B(7,3) and the magnitude of AB.
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Find the magnitude of the vector from the origin to (8,-6) and write the vector as the sum of unit vectors.
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What is the ordered pair representing YZ if Y(5,0) and Z(7,6)? Then find the magnitude of YZ.
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Given vectors u=-9i+8j and v=7i+5j, find 2u-6v in terms of units i and j.
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Given vectors u=7i+3j and v=-4i+3j, find 5u-4v in terms of units i and j.
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Study Notes
Ordered Pairs and Vectors
- Vectors can be represented as ordered pairs (x, y) defined by two points, Y and Z.
- Examples of ordered pairs include:
- For points Y(14,-23) and Z(23,-14), the ordered pair for YZ is (9,9) and the magnitude is (9\sqrt{2}).
- For points Y(4,2) and Z(2,8), the ordered pair is (-2,6) with a magnitude of (2\sqrt{10}).
Magnitude Calculations
- The magnitude of a vector from the origin to a point (x, y) can be calculated using the formula (\sqrt{x^2 + y^2}).
- Example: From origin to (-7,-5), the magnitude is (\sqrt{74}).
- Example: From origin to (8,-6), magnitude calculated is 10.
Vector Representation
- The vector can be expressed as the sum of unit vectors, using i and j notation:
- The vector to (-7,-5) is represented as (-7i - 5j).
- The vector to (8,-6) is shown as (8i - 6j).
Additional Vector Examples
- The vector from A(31,-33) to B(36,-45) is represented as (5,-12) with a magnitude of 13.
- For points A(-9,9) and B(7,3), the vector is (16,-6) with a magnitude of approximately (17.088).
Operations with Vectors
- Vectors can be manipulated through arithmetic operations:
- For vectors (u = -9i + 8j) and (v = 7i + 5j), calculating (2u - 6v) results in (-60i - 14j).
- For vectors (u = 7i + 3j) and (v = -4i + 3j), the expression (5u - 4v) yields (51i + 3j).
Summary of Results
- Key magnitude results:
- (9\sqrt{2})
- (2\sqrt{10})
- (\sqrt{74})
- (10)
- Ordered pairs found for different vectors illustrated throughout the flashcards for practice and understanding.
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Description
Test your knowledge on algebraic vectors with this quiz focused on finding ordered pairs and calculating magnitudes. Challenge yourself with various coordinate points and improve your understanding of vector representation and distance.
