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Problem 45 Medium Difficulty

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

$ x = 2 - 2t $ , $ y = 3t $ , $ z = 1 + t $ ; $ x + 2y - z = 7 $

Answer

$(-2,6,3)$

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Video Transcript

Hello. Precaution is taken from vectors and geometry of the space. And the question is find the equation of lines and planes. Find the question of a find a point at which the line intersect a given page. So that line is X. Is equal to -2 T. Why is equal to tt That is equal to one thirsty. Okay and X plus two Y minors. That is equal to seven. So we need to find a point which which is passing. Uh We need to find a point at which line intersects the plane. So in order to evaluate that point let us execute the value of X. Y. Z out of the line. In the given train equation we get to minus two T. There's two into 20 minus of one plus T. Is equal to seven. If we fail to solve it we get to minus duty last 60 -1 -3 is equal to Sam And for those all we need we get five to minus duties. 20 Plus one is a tradition. Well that's all we need is equal to seven minus 26 of what we that is 2 50 is equal to two then X is equal to 2 -4. So that will be team two minus. To introduce minus to invite is your car too Treaty. So I will be going to so that will be equal to six and said this is equal to one thirsty. That is equal to one plus two which is equal to three. So the given point to which that line intersect with the plane is minus 263, which uses the required points, So Hope disclose her.