00:01
In part a, we want to prove that these three points are the vertices of an isosceles triangle.
00:09
So we need to compute the length of the vector ab, the length of the vector ac, and the length of the vector b.
00:20
The length of the vector ab equals the square root of 1 squared plus minus 1 squared, plus 4 squared, which equals the square root of 18.
00:40
The length of the vector ac equals the square root of 4 squared plus 2 squared plus 4 squared plus 4 squared, which equals the square root of 36, which is 6.
00:56
The length of the vector bc equals the square root of 3 squared plus 3 squared plus 0, square which equals the square root of 18.
01:09
So we know that the nance of ab equals the nance of bc, and hence it is an a socialist triangle.
01:22
In per b, we want to prove these three points are the vertices of a right angle to triangle.
01:32
We can write the vectors ab, which equals minus 1 minus 1 minus 4 and the vector ac is minus 4 to minus 4 the vector bc equals minus 3 0 the dot product of ab and bc equals minus 1 times minus 3 plus minus 1 times 3 plus minus 4 times 0, which equals 0.
02:20
And hence, ab is perpendicular to b -c...