Chapter 10: Q .15. (page 834)

Find the point where the line $x = 鈭� 7, y = t, z = 5$ intersects the $x z -$ plane. Explain why the line does not intersect the other two coordinate planes.

Short Answer

Expert verified

$The required answer is (- 7, 0, 5); the line is parallel to y -axis$

Step by step solution

Step 1:Given information

$the equations x = - 7, y = t, z = 5 .$

Step 2:Calculation

Consider the equations $x = - 7, y = t, z = 5$ .

Take the line $L$ equation.

$x = - 7, y = t, z = 5$

Then, $r (t) = (- 7, t, 5)$

When the line intersects in $x z$ -plane the value of $y = 0$ .

Now substitute $y = 0$ in $y = t$

$t = 0$

Substitute $t = 0 in r (t) = (- 7, t, 5) .$

$r (t) = (- 7, 0, 5)$

Thus the point in

x z

-plane is

(- 7, 0, 5)

The line does not intersect the $x y, y z$ plane as the line is parallel to $y$ -axis. Thus the point where the line intersects the coordinate plane $x z$ is $(- 7, 0, 5) .$ Therefore, the required answer is $(- 7, 0, 5);$ the line is parallel to $y -$ axis

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91影视

Find the point where the line $x = 鈭� 7, y = t, z = 5$ intersects the $x z -$ plane. Explain why the line does not intersect the other two coordinate planes.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

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Find the point where the line x=鈭�7,y=t,z=5 intersects thexz-plane. Explain why the line does not intersect the other two coordinate planes.

Short Answer

Step by step solution

Step 1:Given information

Step 2:Calculation

One App. One Place for Learning.

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Find the point where the line $x = 鈭� 7, y = t, z = 5$ intersects the $x z -$ plane. Explain why the line does not intersect the other two coordinate planes.