00:01
In this question, we are asked to find the area of the triangle with the vertices a, b and c.
00:07
I'll draw a random triangle and let's say its vertices are a, b and c.
00:17
Now what we'll do is we'll create two vectors.
00:21
We'll create the vectors a, b and a, c.
00:30
Now recall that when you take the cross product, then you'll get the area of the parallelogram based on a, b and a, c.
00:38
And to get the area of the triangle, we need to take the one half of that cross product.
00:44
So the area of the triangle equals one half multiplied by the magnitude of the cross product of a, b and a, c.
00:58
Now we need to calculate the vectors a, b and a, c.
01:01
To get a, b, we need to subtract the coordinates of a from the coordinates of b.
01:06
We'll get 8 minus 7, 14 minus 9 and 3 minus 3.
01:14
So and that's gonna be 1, 5 and 0.
01:21
To get the coordinates of a, c, we need to subtract the coordinates of a from the coordinates of c.
01:30
And we'll get the vector with coordinates 6 minus 7, 9 minus 9 and 2 minus 3.
01:41
And that's gonna be the vector with coordinates negative 1, 0 and negative 1.
01:49
Now let's calculate the cross product...