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

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

$\left(\frac{2}{5}, 4,0\right)$

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Johns Hopkins University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Hello. We have a question uh in which we need to find the point at which the line intersects the given plane. This is five X. Equal to or why? By two Equal to their plus two. So this is the line and given plane is 10 x -7. Y Plus three. said equal to plus 24 equals to zero. Place 24 equal to zero. Okay so uh this is let us support this to be lambda. So if we take these two will be having X equal to lambda by five. If it takes these two, why call to to linda these three? Is that equal to a lambda minus two? Okay let us plug in here. And this equation 10 and two lambda by five minus seven into two. Lambda plus three. Lambda minus two Plus 24 equal to zero. These two will get cancelled out to lambda minus 14. Lambda plus three. Lambda minus six Plus 24 equal to zero. So to illustrate in a 5-14 minus nine lambda plus 18 equal to zero. So nine left A will be equal to 18. So lambda will be equal to 18 x nine which is equal to two. So this is the value of lambda. So required points will be from here X equal to lot number five. Yeah two by five. Why equal to two lambda two and two To which is four. And that equal to λ -2, 2 -2 which is zero. So points are two by five. Coming for comma zero. So these are the points. Thank you