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# If $r = \langle x, y, z \rangle$ , $a = \langle a_1, a_2, a_3 \rangle$ and $b = \langle b_1, b_2, b_3 \rangle$ show that the vector equation $(r - a) \cdot (r - b) = 0$ represents a sphere, and find its center and radius.

## Center $\left(\frac{a_{1}+b_{1}}{2}, \frac{a_{2}+b_{2}}{2}, \frac{a_{3}+b_{3}}{2}\right) ;$ radius $\frac{|\mathbf{a}-\mathbf{b}|}{2}$

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##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

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### Video Transcript

The problem is, if our tests go to X y Z A is equal to a one a two a three on being physical Toby one b two b three showed that the factory equation our minus a dot are minus B is equal to zero. Reference fans of the fear and find its center and writers first. Our mind say it's acquit you X minus the one uh, I minus two and C minus three. Our dynasty is for two X minus one. Why must into c minus B three is it? And since our minds a dot I'm speeds, you got zero. So we have X minus the one times X months be one us. Why months? A too Hamzawy minus p too. US C minus three. I have seen my species very. It's equal to zero. And then we have This is ex Claire minus. You want Pastilles? One Thanks us. The one you want us. Why square minus a two Class B too. Time's line us to be too us. The squire minus a three plus three. Come see plus three Very. It's equal to zero. Then we completed Squires. Have X minus a one plus B one must be one squire Us. Why minus et Tu asked me to over to squire plus C minus a three class B three over two square. It's me, conto. They want us to be one squire over for us to pass speech. You squatting over four US A three speed three square. We're four minus. They want you want one of A to be too. When I say three, this is he caught you by force times They want my spee one squire us A to minus B too. Squire us a three minus speed three square. So toe toe equation Armaments ate that are speaking. He's got zero represents A sphere on the center is they want class B one, four, two, two plus two over to a three. Plus the three over, too. Vitus is equal to one half routine stuff they want minus B one square us ain't You might speed too. Squire plus a three minus B three square

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##### Lily A.

Johns Hopkins University

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp