Chapter 10: Q .37. (page 849)

In Exercises 35–38, find an equation of the line of intersection of the two given planes.
$x = 4 and 3 x - 5 y + 2 z = - 3$

Short Answer

Expert verified

The equation of the line of intersection of the two given planes is

r (t) = ⟨ 2 + t, - 3 + 4 t, 5 - 5 t ⟩

Step by step solution

Step 1:Given information

$Consider the points P (2, - 3, 5), Q (3, 1, 0) and R (- 1, 0, 7) .$

Step 2:Calculation

$The equation of the line containing the points A (x_{0}, y_{0}, z_{0}) and B (x_{1}, y_{1}, z_{1}) is given by:$

$r (t) = <x_{0} + a t, y_{0} + b t, z_{0} + c t>$

Where, $⟨ a, b, c ⟩ = <x_{1} - x_{0}, y_{1} - y_{0}, z_{1} - z_{0}>$

$The equation of line containing the points P (2, - 3, 5) and Q (3, 1, 0) is:$

$r (t) = ⟨ 2 + t (3 - 2), - 3 + t (1 + 3), 5 + t (0 - 5) ⟩$

$= ⟨ 2 + t, - 3 + 4 t, 5 - 5 t ⟩$

$Therefore, the equation of line the points P (2, - 3, 5) and Q (3, 1, 0) is$

$r (t) = ⟨ 2 + t, - 3 + 4 t, 5 - 5 t ⟩ .$

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In Exercises 35–38, find an equation of the line of intersection of the two given planes.
$x = 4 and 3 x - 5 y + 2 z = - 3$

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

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In Exercises 35–38, find an equation of the line of intersection of the two given planes.x=4and3x-5y+2z=-3

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Statistics

Decision Maths

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In Exercises 35–38, find an equation of the line of intersection of the two given planes.
$x = 4 and 3 x - 5 y + 2 z = - 3$