Vector Operations and Magnitudes Quiz

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Questions and Answers

Given vectors C = (1, -2) and D = (0, -4), what is the magnitude of vector C - D?

$\sqrt{5}$ (correct)
$\sqrt{10}$
$\sqrt{13}$
$\sqrt{2}$

If vector A + B = (3, -1) and vector A - B = (2, 1), what is the magnitude of vector A?

$\sqrt{2}$
$rac{\sqrt{26}}{2}$ (correct)
$\sqrt{10}$
$\sqrt{rac{29}{2}}$

Given vectors A = (-2, 3) and B = (2, 1), what is the magnitude of vector A - B?

$\sqrt{2}$
$\sqrt{30}$
2$\sqrt{5}$ (correct)
4

Which of the following is a correct representation of the vector sum if A=(3,-1), B=(-2,4), and C=(1,2)?

<p>$(3-2+1, -1+4+2)$ (C)</p> Signup and view all the answers

Given A=(2, 3) and $\vec{A}-\vec{B}=(5, 1)$. Calculate the vector $\vec{B}$

<p>(-3, 2) (C)</p> Signup and view all the answers

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Flashcards

Vector Magnitude

The magnitude of a vector represents its length. It can be calculated using the Pythagorean theorem: |v| = √(x² + y²), where x and y are the x and y components of the vector respectively.

Vector Subtraction

To subtract vectors, subtract their corresponding components. C - D = (Cx - Dx, Cy - Dy).

Magnitude of C - D

The magnitude of a vector is found by calculating the square root of the sum of the squares of its components. |C - D| = √((Cx - Dx)² + (Cy - Dy)²).

Solving for A

Given vector A + B and A - B, we can solve for the vector A by adding the two equations together, then dividing by 2.

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Magnitude of Vector A

The magnitude of vector A (|A|) is calculated using the Pythagorean theorem: |A| = √(Ax² + Ay²).

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Study Notes

Vector Operations and Magnitudes

Vector C-D Calculation:
- Vector C = (1, -2)
- Vector D = (0, -4)
- Vector C - D = (1-0, -2-(-4)) = (1, 2)
- Magnitude of C-D = √(1² + 2²) = √5
Vector A Magnitude Calculation:
- Vector A + B = (3, -1)
- Vector A - B = (2, 1)
- Add the two equations: 2A = (5, 0)
- Vector A = (5/2, 0)
- Magnitude of A = √((5/2)² + 0²) = 5/2 = 2.5
Vector A-B Magnitude Calculation:
- Vector A = (-2, 3)
- Vector B = (2, 1)
- Vector A - B = (-2-2, 3-1) = (-4, 2)
- Magnitude of A-B = √((-4)² + 2²) = √(16 + 4) = √20 = 2√5