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Given the vector v has an initial point at (1,0) and a terminal point at (1,-6), find the exact value of ||v||. Answer:

Given the vector v \mathbf{v} has an initial point at (1,0) (1,0) and a terminal point at (1,−6) (1,-6) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:

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Transformations of absolute value functions: translations and reflectionsright chevron icon

Full solution

Q. Given the vector v \mathbf{v} has an initial point at (1,0) (1,0) and a terminal point at (1,−6) (1,-6) , find the exact value of ∥v∥ \|\mathbf{v}\| .\newlineAnswer:
  1. Understand the 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 plug in the coordinates of the initial and terminal points into this formula to find ∣∣v∣∣||v||.
  2. Substitute Given Points: Substitute the given points into the formula: ∣∣v∣∣=(1−1)2+(−6−0)2||\mathbf{v}|| = \sqrt{(1 - 1)^2 + (-6 - 0)^2}.
  3. Calculate Differences: Calculate the differences: ∣∣v∣∣=(0)2+(−6)2||v|| = \sqrt{(0)^2 + (-6)^2}.
  4. Square the Differences: Square the differences: ∣∣v∣∣=0+36||\mathbf{v}|| = \sqrt{0 + 36}.
  5. Add the Squares: Add the squares: ∣∣v∣∣=36||\mathbf{v}|| = \sqrt{36}.
  6. Take the Square Root: Take the square root: ∣∣v∣∣=6||v|| = 6.

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