Explanation Given: The line passes through the point P = ( 5 , 5 , 2 ) and the direction vector is v = 〈 0 , − 2 , 1 〉 . Formula Used: The vector parameterization for the line is: r ( t ) = P + v t … ( 1 ) where P is a point and v is the direction vector. Calculation: Consider the given point and the direction vector: P = ( 5 , 5 , 2 ) and v = 〈 0 , − 2 , 1 〉 Put these values in equation (1), we get r ( t ) = ( 5 , 5 , 2 ) + t 〈 0 , − 2 , 1 〉 = ( 5 , 5 , 2 ) + 〈 0 , − 2 t , t 〉 r ( t ) = 〈 5 , 5 − 2 t , 2 + t 〉 Now, to get the other vector parameterization of the line, let the direction vector w parallel to the direction vector v :

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ISBN: 9781319050733

Author: Rogawski

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Chapter 13.2, Problem 59E

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We need to find two different vector parameterizations of the line through the given point and the given direction vector.

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Chapter 13.2, Problem 58E

Chapter 13.2, Problem 60E

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We need to find two different vector parameterizations of the line through the given point and the given direction vector.

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We need to find two different vector parameterizations of the line through the given point and the given direction vector.

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