00:01
So, in this question the points a, b, c, d lie in the same plane if and only if their scalar triple product is 0 that is ab vector dot ac vector cross ad vector equals to 0.
00:35
So, first of all we will find ab vector that will be equals to b points that is 3 minus 1 6 then minus coordinates of a that is 1 comma 3 comma 2 and this will be equals to 2 comma minus 4 comma 4.
00:59
Then next will be ac vector.
01:03
So, ac vector will be equals to 5 comma 2 comma 0 minus 1 comma 3 comma 2 equals to 4 comma minus 1 comma minus 2 and next will be ad vector.
01:21
So, ad vector will be equals to 3 comma 6 comma minus 4 and minus 1 comma 3 comma 2.
01:31
So, this will be equals to 2 comma 3 comma minus 6.
01:36
Now, we have to find out scalar triple product.
01:40
So, that will be ab vector dot product ac vector cross ad vector.
01:51
So, this will be equals to determinant of 2 then minus 4 then 4 we are taking these points.
02:01
So, this is 2 minus 4 4.
02:04
So, next point will be 4 minus 1 minus 2 and next will be 2 3 minus 6.
02:12
Now, we will expand the given determinant to find the triple scalar product.
02:17
So, here it will be plus it will be minus and it will be plus...
