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8. Given P(3, -9) and Q(0, -3), find the component form of PQ and PQ.

8. Given P(3, -9) and Q(0, -3), find the component form of PQ and PQ.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 8:** Given the points \( P(3, -9) \) and \( Q(0, -3) \), find the component form of the vector \( \overrightarrow{PQ} \) and its magnitude \( |\overrightarrow{PQ}| \). ### Explanation: To find the component form of the vector \( \overrightarrow{PQ} \), subtract the coordinates of point \( P \) from point \( Q \): - \( x \)-component: \( 0 - 3 = -3 \) - \( y \)-component: \( -3 - (-9) = 6 \) Thus, the component form of \( \overrightarrow{PQ} \) is \((-3, 6)\). To find the magnitude \( |\overrightarrow{PQ}| \), use the formula for the magnitude of a vector: \[ |\overrightarrow{PQ}| = \sqrt{(-3)^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5} \]
Transcribed Image Text:**Problem 8:** Given the points \( P(3, -9) \) and \( Q(0, -3) \), find the component form of the vector \( \overrightarrow{PQ} \) and its magnitude \( |\overrightarrow{PQ}| \). ### Explanation: To find the component form of the vector \( \overrightarrow{PQ} \), subtract the coordinates of point \( P \) from point \( Q \): - \( x \)-component: \( 0 - 3 = -3 \) - \( y \)-component: \( -3 - (-9) = 6 \) Thus, the component form of \( \overrightarrow{PQ} \) is \((-3, 6)\). To find the magnitude \( |\overrightarrow{PQ}| \), use the formula for the magnitude of a vector: \[ |\overrightarrow{PQ}| = \sqrt{(-3)^2 + 6^2} = \sqrt{9 + 36} = \sqrt{45} = 3\sqrt{5} \]
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