Explanation Given: ( x 1 , y 1 , z 1 ) = ( − 4 , − 2 , 1 ) , ( x 2 , y 2 , z 3 ) = ( − 2 , − 2 , 3 ) Definition used: The position vector P Q ⇀ is 〈 x 2 − x 1 , y 2 − y 1 , z 2 − z 1 〉 . Formula used: The equation of the line through the point P 0 ( x 0 , y 0 , z 0 ) to Q 0 ( x 0 , y 0 , z 0 ) is given by r 1 ( t ) = r 0 + t v . Calculation: Let r ( t ) be the required equation of line. Let r 0 be the position vector of the point P ( − 4 , − 2 , 1 ) and is given as, r 0 = O P → = 〈 − 4 , − 2 , 1 〉 To compute the position vector from P ( − 4 , − 2 , 1 ) to Q ( − 2 , − 2 , 3 ) as follows,

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ISBN: 9780135182543

Author: Briggs

Publisher: PEARSON

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Chapter 14.1, Problem 14E

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To find: A function r(t) for the line passing through P(−4,−2,1) to Q(−2,−2,3).

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A function r ( t ) for the line passing through P ( − 4 , − 2 , 1 ) to Q ( − 2 , − 2 , 3 ) .

Solution Summary: The author explains how to find the function r(t) for the line passing through the point.

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To find: A function r(t) for the line passing through P(−4,−2,1) to Q(−2,−2,3).

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