Assessment due mon j resources hint submit answer question 7...

Assessment Due: Mon, J Resources Hint Submit Answer Question 7 of 13 Give an equation for the sphere with diameter $\overline{PQ}$, where $P = (1,1,-5)$ and $Q = (1,7,1)$. Express numbers in exact form. Use symbolic notation and fractions where needed.) equation: Publisher: W.H. Freeman

Transcript

00:01 In this question we're asked to find an equation for the sphere with diameter pq, where p is this point and q is this point.

00:09 So let's just recall that the equation for the sphere will be x minus x of the center point squared plus y minus y center point squared plus z minus z center point squared equals r squared, where so the point x, c, y, c, z, c, is.

00:31 The center of the sphere and r is a radius.

00:36 Right, so we need to calculate two things.

00:38 The first thing is the center which we need to use p and q for and the second thing is the radius.

00:44 So let's start with the center, right? so the center c will be the point.

00:50 If p and q form a diameter, it means that they pass through the center and the average between p and q will be our center point.

01:00 So this is the code, the point.

01:01 Point with coordinates being the average of each of the coordinates of p and q between p and q.

01:07 So this will be first coordinate 1 plus 1 over 2, second coordinate 1 plus 5 over 2, third coordinate minus 7 plus 1 over 2, which is 1 plus 1 is 2 over 2 is 1, 1 plus 5 is 6 over 2 is 3, minus 7 plus 1 is minus 6 over 2, minus 3.

01:30 So this is the center.

01:31 And the radius will, of course, be half of the distance.

01:35 If p and q is a diameter, the radius is half a diameter.

01:39 So it will be 1 over 2 the distance between p and q.

01:45 Right? we want r squared.

01:47 So let's just square everything...