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Find a nonzero vector parallel to the line of intersection ofthe two planes 5x+y-3z=2 and 2y-x=-3...

Question

Find a nonzero vector parallel to the line of intersection ofthe two planes 5x+y-3z=2 and 2y-x=-3

Find a nonzero vector parallel to the line of intersection of the two planes 5x+y-3z=2 and 2y-x=-3



Answers

Find a vector parallel to the line of intersection of the planes given by $2 y-z=2$ and $-2 x+y=4$

In this question we are given with their two vectors. Yes, sorry. With the two recreational plane, the first plane is core X -3 Y. And yes. Who? That is equal to well. And the third one is X plus Y, Y -30 equals to 25. This is your first learn and this is your second plane. We have to find a factor that is parallel to the line of the intersection of the both of the place. The first of all, I am going to write the normal workers of both of the plane. Normal vector to the first plane, normal vector to the second plane. That is coefficients of X. Y ended Means for I -3 D. Last. Okay. And for the 2nd 1. With that here I And Bless of five J. and- of K. Now we know that we have to find a vector but alert to line up in intersection, we can say that a letter. That is but a logical line of intersection. Short way equals two. But Bangui. Fuller to work to anyone. And vector angle means it is that. And then do that. Boss would appear because there is a cross product that is perpendicular to anyone. And And so we have to make the cross product of vector anyone and vector. And to with the help of determinant, I'm going to make the cross product. Okay in the festival we are to make I J. K. In the second row. We have to substitute the coefficient of vector and one vectors That are 4 -3 and two in the second will be able to substitute 1, 5 and -1. Now we have to make the expo engineer so you can see there dear I into 3 -10. -AJ. into -4 -2 and less. Gay into 20 last three. Now this turns out into minus 79 And the last six a day And the last 23 K. So this is the required answer of this given question. Okay, I can say that this is the required vector for this question. Okay, thank you.

In this question we are given with evacuation of two planes. I'm going to write the equation of both the planes. First plane is I can say that Works -3 Way and plus 5 30. That close to two. And the second plan is four X plus Hawaii and minus that. Is that Music was 2 7. First of all, I am going to write the normal workers of both blends here. Okay. Normal vector of past planets. We can expect to anyone and second, but there is weakness and that is a component. So X. Y. That needs to minus three and five. And in the 2nd 13 days 41 and minus three. Now we have to find out what that that is that. And then cool line of intersection and we know that dates that should they definitely. But then the bowler too that have anyone and victor. And to and to find a vector that is perpendicular to both the vectors. We have to make the cross product. So I'm going to make that prospered appear okay with the help of a determinant that takes in the first row, I j K in the second row, components of vector anyone That are 2 -3, 5. In the Third World, it takes components of and 2, 4, 1 and -3. Okay? No, we are to expand it. So we are trying to 9 -5 years and then we get minus Day into -6 -20 and plus gay into so plus 12. But that I can say that after simplifying it, I get four I right Less of 26 a day and bless off for being gay. So this is the answer of the given Bush in here. Okay, thank you.

Hello there. So for this exercise we have 1.2 ventures that are probably to some plane. And the plane passed through the zero. So the geometric idea of this is that you have here, the space X, the Y and zero defined a point In the space right at zero. And through this point we have a plane. But this plane has to pearl vectors. Let's go to be one. And we need to. So basically the idea is that these two vectors expand this plane that passed through this zero. So the equation of this plane Is then given by two parameters TNS. And that is equal to zero point where this plane is passing through plus three times the first vector to this parallel plus s times the second vector. That is probably an important thing here. Is that these two vectors should be non cleaner. Otherwise we are having problems because basically B one is probably to be too, they will define another plane. But a line. Okay, So that's an important remark. So we just need to replace the data to the equation of this plane. So we have the days it's going to be equals to 06 -2 Plus T. Times zero nine minus one plus S 0 -30. And then we just need to put all together and we obtain the vector zero six plus 90 minus three S. There's a plus and minus two minus T. And there's a parametric equation of the plane defined by this point and parallel to these two vectors.

We have given to any questions. Q minus express to wait splices It is equal to one, and our express fireplace there is equal to zero. We need to find the plane or the line of the plane, which is we need to find the question the plane which does the intersection off you in our. So that's all this exercise we need to find the normal that this is the plane which is, and cue coefficients off x crazy and we get and not one comma one come up. One knowledge This would finally go on one point. So step one, find it on one point, put their visible to zero. We get to a question minus X plus two y is equal to one and express why is equal to zero. So I get three very easy gold one. So they oppose my wise one by three and X is he going to minus way? But they're poor eggs. Is it going toe minus one by three. So we get one point, which is one Goma three with a negative sign. Come on. Coma 30 Never been planned. E prosper ducked off and being do and you know we'll do the cross product off and you and do, and that it is equal to dominant off I d g my list 1 to 1 and 111 So this is equal to I in dude. Do minus one minus day into minus on minus one was into minus one. Going minus tool. This is the Goto I bless O. J minus three. Now we have one point as my last one comma tree from one comma tree comma zero and one point we got as one comer two comma minus tree From this question, no question Off the line is given us se r p is equal to It's not Why not? Said not bless de into a gonna be ponsi ville Explored by noted no represents the equations from the be not and when tu minus three years, ABC villages. And so we get our d az minus one by 31 but three from a zero Lestienne do one going to come on. My history says it's four to minus one by three congruent by three from a zero plus the duty minus treated. So does come by next crazy points we get minus one by three Rusty number one by three Blessed duty Goma minus three D So I get X is equal to minus one by three plus t by easy good one by three plus two D and that doesn't go to minus three ts my ourselves.


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