Explanation Given: r 1 ( t ) = t 〈 2 , 1 , 3 〉 r 2 ( t ) = ( − 6 , − 3 , − 9 ) + t 〈 8 , 4 , 12 〉 Formula Used: The vector parameterization for the line is: r ( t ) = P + v t … ( 1 ) where P is a point ( x , y , z ) and v is the direction vector 〈 a , b , c 〉 . Calculation: Here, the direction vector of r 1 is v = 〈 2 , 1 , 3 〉 And, the direction vector of r 2 is w = 〈 8 , 4 , 12 〉 Now, w = 〈 8 , 4 , 12 〉 = 4 〈 2 , 1 , 3 〉 = 2 v Thus, the direction vectors v and w are parallel. Here, r 1 ( t ) can be rewritten as: r 1 ( t ) = ( 0 , 0 , 0 ) + t 〈 2 , 1 , 3 〉 Now, we need to show that r 2 ( t ) passes through the point ( 0 , 0 , 0 ) ...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 13.2, Problem 58E

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We need to show that $r_{1} (t)$ and $r_{2} (t)$ define the same line.

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Chapter 13.2, Problem 57E

Chapter 13.2, Problem 59E

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We need to show that r 1 ( t ) and r 2 ( t ) define the same line.

Solution Summary: The author proves that the lines r 1 (t ) and 2 ( t) define the same line. The vector parameterization for the line is P + v

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We need to show that $r_{1} (t)$ and $r_{2} (t)$ define the same line.

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Chapter 13 Solutions

We need to show that r 1 ( t ) and r 2 ( t ) define the same line.

Solution Summary: The author proves that the lines r 1 (t ) and 2 ( t) define the same line. The vector parameterization for the line is P + v

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We need to show that r1(t) and r2(t) define the same line.

Want to see the full answer?

Chapter 13 Solutions

We need to show that $r_{1} (t)$ and $r_{2} (t)$ define the same line.