Q .15. - Calculus

Question

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

Step-by-Step Solution

Answer

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

Step 1:Given information

$\text{ the equations }x=-7,y=t,z=5\text{. }$

Step 2:Calculation

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

Take the line$\mathcal{L}$ equation.

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

Then,$r\left(t\right)=(-7, t, 5)$

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

Now substitute $y=0$ in$y=t$

$t=0$

Substitute$t=0\text{ in }r\left(t\right)=(-7,t,5)\text{. }$

$r\left(t\right)=(-7,0,5)$

Thus the point in $xz$-plane is $(-7,0,5)$.

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