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Chapter 12.5, Problem 46E
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### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Find the point at which the line intersects the given plane.46. x = t − 1, y = 1 + 2t, z = 3 − t; 3x − y + 2z = 5

To determine

To find: The point at which the line with parametric equations x=t1,y=1+2t,z=3t intersects the plane 3xy+2z=5 .

Explanation

The point of intersection of the line and the plane is determined by substituting the value of the scalar parameter (t) in the parametric equations of the line.

The scalar parameter is determined by substituting the parametric equations in the equation of the plane.

Write the parametric equations of the line as follows.

x=tâˆ’1,â€‰y=1+2t,â€‰z=3âˆ’t (1)

Write the equation of the plane as follows.

3xâˆ’y+2z=5 (2)

Calculation of scalar parameter (t) :

Substitute (tâˆ’1) for x , (1+2t) for y , and (3âˆ’t) for z in equation (2),

3(tâˆ’1)âˆ’(1+2t)+2(3âˆ’t)=5

Solve the expression

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