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Problem 22 Easy Difficulty

Determine whether the lines $ L_1 $ and $ L_2 $ are parallel, skew, or intersecting. If they intersect, find the point of intersection.

$ L_1 : \frac{x}{1} = \frac{y - 1}{-1} = \frac{z - 2}{3} $
$ L_2 : \frac{x - 2}{2} = \frac{y - 3}{-2} = \frac{z}{7} $

Answer

skew

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Video Transcript

mhm. In the question they're asking to determine whether line L. One and L two, our palates you are intersecting if intersecting them, Find the point of intersection line L one and L two is given by the equation X by one equal to y minus one or minus one is equal to zed minus two by three. And lt is given by x minus two by two is equal to y minus three by minus two is equal to zero by seven. And if we put the equation in a arrange manner then we can get no value to be created to all constant value that is equal to L one which equals to constant value T. And L two which equals to constant value S. And so For the first conditioner to take L one and L two is parallel or not. Therefore From L one equation can find that X equal to t. Why equal to minus t plus one That equal to 3? T. Let's do. And yeah For equation L two We get x equal to two x plus two. Why equal to -2? s plus three that equal to seven is yeah. Therefore for checking if these lines are value to each other, not to complete the coefficients of border lines. So this is equal to one x 2 is equal to -1 x -2 is equal to three x 7. But the third ratio is not equal to the first ratios. Hence L one and L two is not Berlin to each other. Now the second part is we have to say whether they are intersecting or not. So we're checking this, you have to compute the X, Y and Z coordinates to be equal and find a valid value. If it has a valid value then they are intersecting. Otherwise they are not intersecting. So the tree equations from these lines rT is equal to To S Plus two. Three, T plus two is equal to seven is and -D. Plus one Is equal to -2 ways plus three. Therefore These are the three questions From the three coordinates of the two lines. So from one we get the value of in terms of s. And if you put this value in the other equation we get mhm minus To S Plus two. Last one is equal to minus two X plus three from this equation. We can derive that -1 is equal to three and this is not possible. Hence these lines are not intercepting since L one and L two is not intersecting. Therefore yeah, L one and L two is a schooling So L one and L two, R. Not Berlin and L one and L two R. Not intersecting also. So L one and L two lines are skew lines and this is the required answer or the given question. Okay