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Given the vector v has an initial point at (8,8) and a terminal point at (8,6), find the exact value of ||v||. Answer:

Given the vector v \mathbf{v} has an initial point at (8,8) (8,8) and a terminal point at (8,6) (8,6) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:

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Full solution

Q. Given the vector v \mathbf{v} has an initial point at (8,8) (8,8) and a terminal point at (8,6) (8,6) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:
  1. Apply Formula: The magnitude of a vector vv with initial point (x1,y1)(x_1, y_1) and terminal point (x2,y2)(x_2, y_2) is given by the formula ∣∣v∣∣=((x2−x1)2+(y2−y1)2)||v|| = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}. We need to apply this formula to the given points to find ∣∣v∣∣||v||.
  2. Substitute Points: Substitute the given points into the formula: initial point (8,8)(8,8) and terminal point (8,6)(8,6). This gives us ∣∣v∣∣=((8−8)2+(6−8)2)||v|| = \sqrt{((8 - 8)^2 + (6 - 8)^2)}.
  3. Calculate Differences: Calculate the differences: (8−8)2=02=0(8 - 8)^2 = 0^2 = 0 and (6−8)2=(−2)2=4(6 - 8)^2 = (-2)^2 = 4.
  4. Substitute Values: Substitute these values into the magnitude formula: ∣∣v∣∣=(0+4)||v|| = \sqrt{(0 + 4)}.
  5. Simplify Expression: Simplify the expression: ∣∣v∣∣=4||\mathbf{v}|| = \sqrt{4}.
  6. Calculate Square Root: Calculate the square root of 44: 4=2\sqrt{4} = 2.

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