Curve-plane intersections Find the points (if they exist)

Chapter 12, Problem 76E

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QUESTION:

Curve-plane intersections  Find the points (if they exist) at which the following planes and curves intersect.

8x+15y+3z=20 ; \(\mathbf{r}(t)=\langle 1, \sqrt{t},-t\rangle\), for t>0

Questions & Answers

QUESTION:

Curve-plane intersections  Find the points (if they exist) at which the following planes and curves intersect.

8x+15y+3z=20 ; \(\mathbf{r}(t)=\langle 1, \sqrt{t},-t\rangle\), for t>0

ANSWER:

Solution 76E

Step 1 of 4:

In this problem we need to find the points (if they exist) at which the following planes and curves intersect. 8x + 15y+ 3z = 20; r(t) = 〈1, , −t〉, for t > 0

Given plane: 8x + 15y+ 3z = 20 and curve 

We have

Therefore

Now plug the values of in 8x + 15y+ 3z = 20 we get

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