00:01
As for the question, we need to define triple product of three vectors.
00:18
So here, for defining it, let x, comma, y, comma, z are the three vectors.
00:36
The scalar triple product of three vectors x, comma, y, comma, z is the scalar product of vector x with the cross product of the vectors of the vectors y and z that is we have x dot product with cross product of y and z so here this will be the required definition for the triple product of three vectors.
02:02
Now we need to show that vectors lie in the same plane if and only if their triple product is zero.
02:36
So here to show this we need to show that any vector, let's say, w, dot product with n to be equals to 0.
02:56
So here, suppose we take w is equals to 1 .2 .3.
03:09
And always, n will be equals to cos 90.
03:22
That will be equals to 0.
03:25
So here we have w at a place of n will put cos 90.
03:35
It will be equals to 0.
03:38
Now since when we put w is equal to 1 comma 2 comma 3 and we know that cost 90 is 0, so here we are getting 0.
03:48
So here we have proved that vector lie in the same plane if and only if there triple product is 0.
04:23
So here this will be the required proof of it...