Q. Given the vector v has an initial point at (0,2) and a terminal point at (−1,2), find the exact value of ∥v∥.Answer:
Calculate Distance Formula: To find the magnitude of vector v, we need to calculate the distance between its initial and terminal points using the distance formula for points in a 2D space: ∣∣v∣∣=((x2−x1)2+(y2−y1)2), where (x1,y1) is the initial point and (x2,y2) is the terminal point.
Substitute Coordinates: Substitute the coordinates of the initial point (0,2) and the terminal point (−1,2) into the distance formula: ∣∣v∣∣=((−1−0)2+(2−2)2).
Calculate Squares: Calculate the squares of the differences: ∣∣v∣∣=(−1)2+(0)2.
Simplify Squares: Simplify the squares: ∣∣v∣∣=1+0.
Add Values: Add the values inside the square root: ∣∣v∣∣=1.
Take Square Root: Take the square root of 1: ∣∣v∣∣=1.
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