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Find the points where the line

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

intersects each of the coordinate planes

Short Answer

Expert verified

The required answer is(0,-9,1)92,0,-1714,-172,0.

Step by step solution

01

Step 1:Given information

The line is

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

02

Step 2:Calculation

Consider the lineLdetermined by the equationsx=t+2,y=2t-5,z=-4t-7.

Take the lineLequation.

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

Then,

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

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

Now substitutex=0inx=t+2.

0=t+2

t=-2

Substitutet=-2inr(t)=(t+2,2t-5,-4t-7).

r(-2)=(0,2·-2-5,-4·-2-7)

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

Thus the point inyz-plane is(0,-9,1)

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