00:01
In this question we have to find equation of plane that is passing through three points.
00:05
I am going to write these given three points.
00:08
Let denote them by abc.
00:10
A point is 3 ,4, 2 and b point is having coordinates minus 2 .1 .0 and c point is having 0 to 1 .1.
00:22
First of all, with the help of these points, we are going to find vector a, b, and vector a .c that lies in the point.
00:30
We have to subtract a from b so we get minus 2 minus 3 i and then 1 minus 4 j and then 0 minus 2k so you can see we get here minus 5i or it can be simply written as in the form of minus 5 comma minus 3 comma minus 2 okay now similarly to find ac we have to subtract a from c so we get here 0 minus 3 i and then 2 minus 4 j and then 1 minus 2 k so you can see that we got here minus 3 and then minus 2 and then minus 1 so these are the vectors that lie in the plane now we need the normal vector of the plane that is vector n we can see that this should be equals to cross product of ab and ac so we have to make the cross product with the help of the determinant that takes ijk in the first row, in the second row minus 5, minus 3, minus 2, in the third row components of ac, that is minus 3, minus 2, minus 1.
01:43
Now, after making the expansion, we get here the normal vector that is equals to minus i plus j plus k, or it can be written as minus 1 .1 .1...