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Find the point where the line x=7,y=t,z=5 intersects thexz-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 toy-axis

Step by step solution

01

Step 1:Given information

the equationsx=-7,y=t,z=5.

02

Step 2:Calculation

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

Take the lineLequation.

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

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

When the line intersects inxz-plane the value of y=0.

Now substitute y=0iny=t

t=0

Substitutet=0inr(t)=(-7,t,5).

r(t)=(-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

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