Question

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

Short answer

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

Step-by-step solution

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