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(1 point) Find the point at which the line (5,-2,-4) + t(1,2,-2) intersects the plane ~Sx L 2y - z = -52_...

Question

(1 point) Find the point at which the line (5,-2,-4) + t(1,2,-2) intersects the plane ~Sx L 2y - z = -52_

(1 point) Find the point at which the line (5,-2,-4) + t(1,2,-2) intersects the plane ~Sx L 2y - z = -52_



Answers

Find the point at which the line intersects the given plane.

$ 5x = \frac{y}{2} = z + 2 $ ; $ 10x - 7y + 3z + 24 = 0 $

Here in this problem, we have given line, so I'm just writing that tax present five packs is equal to y by two is equal to that pledge to now Playing can be written edged 10 x minus seven y plus three. Jet plus 24 is equal to zero. Rated B. Question one Rated B Question, too. Now write the Parametric equation of the line so I can write the express an edge. Five packs is equal to T. Why buy two is equal to t that plus two is equal to t. So access coming at be by five Why is equal to two t and yard is equal to t minus two. So let it be question number three now going forward and solving it further So I can died Dan X minus seven y plus three Jad plus 24 is called to zero. So just putting the value here. So 10 multiplication three by five minus seven Multiplication to t plus three multiplication T minus to plus 24 is equal to zero. So simplifying it I get 90 is equal to 18. So t is coming edge too. So this is the point of intersection when he is equal to two. So the value of X is equal to T by five, which is equal to two by five. Why is equal to two T, which is equal to two? Multiplication two is equal to four and they are difficult to to minus two, which is equal to zero. Now I'm just writing the point of intersection, so point of intersection is given by two by five 40 This is the point of intersection at which line one intersected plane too.

In this question, will Even the question line will have XY code. You want trust duty? Why? In coaching one crust five t the Inco Jude three day. And we have the question that plan Well, we have the express. Why press see e code to do so? To find a question, uh, to find a partner intersection. We're going to look in those volume the X prize into this plan. So if we end up everything with a ghenda going trust you d plus one past five p plus Thrity in, we can teach you so it will signify this one again. That 10 day in we go do? Yeah, and we could use their Oh, they're funded Teoh quiches. Zero. With the equal Jizo, you can find a partner intersection. It would be 20. Which is it gonna 110 here

Given the question That line where we have the accident got u minus one plus three day. Why, in coaching the man is true with the culture of five D and the question the plan. We'll have that too. Thanks, Ministries. The co 27 So I only need to do is we're looking this exercise in today Question the plan. You have it You x now minus one. Blessed Treaty Ministry. Xena acquitted of five p equal to seven. So it was assumed if I'm gonna managed to last six day Manus fitting the ICO to seven. So again, this one b minus 90. Enrico Teoh on and I so todo go to minus one. Quit a secret U minus one. You can find a problem. The intersection. It would be a world in which a minus one will have this and we'll be the man is far Finest you for the wine and see a coach a minus five

Mhm. For the given problem, we see that We're gonna have the vector 5. 3 Euro. And then we have the point for -1, based on the parametric equations? Or is the symmetric equations. And then we also have 2 -3. I get five is the other normal vector. But we see that the intersection point between the plane and the line. If we plugged in this point, for example, We would end up getting four times five is 20 um negative one times three is negative three, so 20 minus three is 17. So this point right here does satisfy the given equation. Um and we see that since we have four negative one, it doesn't matter what the Z coordinate is. It could be an easy coordinate, but as long as we have four negative one, it will be satisfied.


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