/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 How do you compute \(|\overright... [FREE SOLUTION] | 91影视

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Chapter 12: Problem 13

How do you compute \(|\overrightarrow{P Q}|\) from the coordinates of the points \(P\) and \(Q ?\)

Short Answer

Expert verified
Answer: The formula for calculating the magnitude of the vector formed by two points P(x1, y1) and Q(x2, y2) is given by |PQ| = 鈭�((x2 - x1)^2 + (y2 - y1)^2).

Step by step solution

01

Identify the Coordinates of P and Q

Let's denote the coordinates of the points P and Q as \(P(x_1, y_1)\) and \(Q(x_2, y_2)\), respectively.
02

Calculate the Differences in X and Y Coordinates

To find the components of the vector \(\overrightarrow{PQ}\), we need to find the differences in the x and y coordinates. The difference in x coordinates is represented by \((x_2 - x_1)\), and the difference in y coordinates is represented by \((y_2 - y_1)\).
03

Use the Distance Formula to Calculate the Magnitude of the Vector

We will now apply the distance formula to compute the magnitude of the vector \(\overrightarrow{PQ}\). The distance formula is given by: $$| \overrightarrow{PQ} | = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
04

Calculate the Magnitude of the Vector

Now, substitute the differences in x and y coordinates from Step 2 into the distance formula and compute the magnitude of the vector \(\overrightarrow{PQ}\). $$|\overrightarrow{PQ}| = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}$$ The result will be the magnitude of the vector \(\overrightarrow{PQ}\), which represents the distance between points \(P\) and \(Q\).

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Most popular questions from this chapter

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