00:01
In this problem, we have been given the vertices of a quadrilateral abcd.
00:04
We need to prove that it is a parallelogram.
00:07
So first of all, let's find the vectors representing the sides of the quadrilateral.
00:11
First of all, consider ab.
00:13
This will be the position vector of b minus the position vector of a.
00:16
Now b has the coordinates negative 3, negative 1, 17.
00:20
So this will be the required position vector.
00:23
We subtract the position vector of a.
00:25
We have 0, 3, 5.
00:26
Now to find the difference between these two vectors, we're going to find the differences between the corresponding components.
00:33
So negative 3 minus 0, then negative 1 minus 3, then 17 minus 5.
00:38
So we end up with negative 3, negative 4.
00:42
Now next we are going to determine bc.
00:45
So we have the position vector of c and from this we subtract the position vector of.
00:53
So we have 4 minus negative 3, that's 4 plus 3 which is 7, then negative 3 minus negative 1, so negative 3 plus 1, so that's negative 2, and then we have 15 minus 17, so we have negative 2.
01:06
And then after this, we are going to determine cd.
01:11
So we have the position vector of d, that's 7, 1, 3, minus the position vector of c, that's 4, negative 3...