Chapter 10: Q .38. (page 849)

In Exercises 35–38, find an equation of the line of intersection of the two given planes.
$x - 2 z = 7 and x - 3 y - 4 z = 0$

Short Answer

Expert verified

The equation is $r (t) = ⟨ 2 - 3 t, - 3 + 3 t, 5 + 2 t ⟩ .$

Step by step solution

Step 1:Given information

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

Step 2:Calculation

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

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

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

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

$The equation of line containing the points P (2, - 3, 5) and R (- 1, 0, 7) is:$

$r (t) = ⟨ 2 + t (- 1 - 2), - 3 + t (0 + 3), 5 + t (7 - 5) ⟩$

$= ⟨ 2 - 3 t, - 3 + 3 t, 5 + 2 t ⟩$

$Therefore, the equation of line the points P (2, - 3, 5) and R (- 1, 0, 7) is$

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

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In Exercises 35–38, find an equation of the line of intersection of the two given planes.
$x - 2 z = 7 and x - 3 y - 4 z = 0$

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

One App. One Place for Learning.

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In Exercises 35–38, find an equation of the line of intersection of the two given planes.x-2z=7andx-3y-4z=0

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

Probability and Statistics

Geometry

Statistics

Calculus

Discrete Mathematics

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.
$x - 2 z = 7 and x - 3 y - 4 z = 0$