Chapter 10: Q .13. (page 834)

Find the points where the line
$x = t + 2, y = 2 t - 5, z = - 4 t - 7$
intersects each of the coordinate planes

Short Answer

Expert verified

$The required answer is (0, - 9, 1) (\frac{9}{2}, 0, - 17) (\frac{1}{4}, \frac{- 17}{2}, 0) .$

Step by step solution

Step 1:Given information

The line is

$x = t + 2, y = 2 t - 5, z = - 4 t - 7$

Step 2:Calculation

$Consider the line L determined by the equations x = t + 2, y = 2 t - 5, z = - 4 t - 7 .$

$Take the line L equation.$

$x = t + 2, y = 2 t - 5, z = - 4 t - 7$

Then,

$r (t) = (t + 2, 2 t - 5, - 4 t - 7)$

When the line intersect in yz-plane the value of $x = 0$

$Now substitute x = 0 in x = t + 2 .$

$0 = t + 2$

$\Rightarrow t = - 2$

$Substitute t = - 2 in r (t) = (t + 2, 2 t - 5, - 4 t - 7) .$

$r (- 2) = (0, 2 \cdot - 2 - 5, - 4 \cdot - 2 - 7)$

$r (- 2) = (0, - 9, 1)$

$Thus the point in y z -plane is (0, - 9, 1)$

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Find the points where the line
$x = t + 2, y = 2 t - 5, z = - 4 t - 7$
intersects each of the coordinate planes

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

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Find the points where the linex=t+2,y=2t-5,z=-4t-7intersects each of the coordinate planes

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

Mechanics Maths

Probability and Statistics

Discrete Mathematics

Decision Maths

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the points where the line
$x = t + 2, y = 2 t - 5, z = - 4 t - 7$
intersects each of the coordinate planes