00:01
Suppose that you stand at the point 5, 6, 0, 5, 6, 0 and you look in direction towards the point that is not visible because it is behind the ball.
00:12
You would then be looking at the point at the sphere.
00:15
If you're standing at point 5, 6, 0 and you're looking at the direction towards the point minus 4, minus 5, 1.
00:24
Find the point on the sphere at which you'll be looking.
00:28
So by looking for points x, y and z.
00:31
So the distance of 5, 6, 0 from 0, 0, 0 would be r is equal to the square root of 5 minus 0 squared plus 6 minus 0 squared which is the square root of 61.
00:47
So the equation of the sphere centred at 0, 0, 0 with the radius r would be x squared plus y squared plus z squared which is r squared equals to 61.
01:02
Now the equation of the line to the point 5, 6, 0 and in the direction of minus 4, minus 5, 1 would be 5, 6, 0 plus t open bracket minus 4, minus 5, 1 minus 5, 6, 0 equal to 5, 6, 0 plus t open bracket minus 9, minus 11, 1 and this is equal to 5 minus 9t comma 6 minus 11t comma t.
01:51
So this line would intersect the sphere if 5 minus 9t squared plus 6 minus 11t squared plus t squared is equal to 61...