Explanation Given: Let L be the intersection of the planes x + y + z = 1 and x + 2 y + 3 z = 1 . Formula used: The parametric equation of the line passing through a point and with direction vector is: x = x 0 + a t y = y 0 + b t z = z 0 + c t Where P 0 = ( x 0 , y 0 , z 0 ) is the point and v = 〈 a , b , c 〉 is the direction vector. Calculation: Consider the two equation of the plane, x + y + z = 1 … (1) x + 2 y + 3 z = 1 … (2) Find the line of the intersection L of both equations (1) and (2). Firstly, find the direction vector to L . We know that, the direction of a line that is formed by the intersection of the planes is the cross product of their normal vectors. Let the vectors n 1 × n 2 is the direction of L . The normal vector to the plane (1) and (2), n 1 = 〈 1 , 1 , 1 〉 and n 2 = 〈 1 , 2 , 3 〉 Direction vector is: n 1 × n 2 = | i j k 1 1 1 1 2 3 | = i ( 3 − 2 ) − j ( 3 − 1 ) + k ( 2 − 1 ) = i − 2 j + k Thus, the direction vector of the line L is n = 〈 1 , − 2 , 1 〉 ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 13.5, Problem 66E

To determine

Find a point $P$ on $L$ by inspection, and write down the parametric equations for $L$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.5, Problem 65E

Chapter 13.5, Problem 67E

Students have asked these similar questions

Let L. be the line with parametric equations x=-9-t y=-8-31 ==-1+2t Find the vector equation for a line that passes through the point P-(-6, -8,-6) and intersects L at a point that is distance 4 from the point Q- (-9,-8,-1). Note that there are two possible correct answers. Use the square root symbol where needed to give an exact value for your answor 000 000 0+10 lat je

write the equation of the line passing through P with direction vector d in (a) vector form and (b) parametric form.

Find parametric equations for the line that passes through the point (−3, 7) and is perpendicular to the vector <6,−8>.

Chapter 13 Solutions

CALCULUS (CLOTH)

Ch. 13.1 - Prob. 1PQ Ch. 13.1 - Prob. 2PQ Ch. 13.1 - Prob. 3PQ Ch. 13.1 - Prob. 4PQ Ch. 13.1 - Prob. 5PQ Ch. 13.1 - Prob. 6PQ Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Find a point P on L by inspection, and write down the parametric equations for L .

Solution Summary: The author explains the parametric equations of the line passing through a point and with direction vector.

Videos

Find a point $P$ on $L$ by inspection, and write down the parametric equations for $L$ .

Want to see the full answer?

Chapter 13 Solutions

Find a point P on L by inspection, and write down the parametric equations for L .

Solution Summary: The author explains the parametric equations of the line passing through a point and with direction vector.

Videos

Find a point P on L by inspection, and write down the parametric equations for L.

Want to see the full answer?

Chapter 13 Solutions

Find a point $P$ on $L$ by inspection, and write down the parametric equations for $L$ .