00:01
Welcome back to another cross products problem were given three points in three d.
00:06
Space and we're asked to find victor orthogonal to the plane created by those three points.
00:15
So one of the things we can do is given these three points.
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We can find two vectors, say pq and pr and since we have two vectors in the plane, the cross product between them is going to be perpendicular to that plane.
00:33
So pq is just q minus p.
00:37
That's going to be 4 0.
00:41
It's for to minus zero, which is two and zero minus negative three, which is just three.
00:52
Similarly pr is ar minus p three minus zero, three minus zero, one minus negative three.
01:04
We can plug these vectors into our matrix here for two, three and three three, four.
01:14
And then use the technique outlined in our textbook defined pq cross pr so remember we ignore the first column of this matrix and then look at two times 4 and it's three times 3, two times 4 -3 times three i minus.
01:43
Then we ignore the second column four times four and it's three times 3 it's for -3 times three j.
01:56
Plus.
01:57
And then we ignore the third column and we'll look at four times 3 -2 times three three -2 times three.
02:10
Okay, simplifying this a little bit two times four is eight, three times 3 is nine.
02:18
So we're looking at negative one in our first coordinate four times 4 is 16, three times 3 is nine, 15 -97...
8 comments
Susan H.
March 5, 2023
Numerade was a massive help
Lynn M.
March 16, 2023
this is seriously the best study aid ive found
Karen L.
June 2, 2023
If I get accepted to school again in the fall, I'm definitely using this again.
Anna H.
July 5, 2023
the answers were on point.
Shawn Z.
August 3, 2023
It helped a ton
Casey O.
November 20, 2023
Wow Dylan really broke down the process of finding a vector orthogonal to the plane formed by those three points Its great to see the stepbystep approach using cross products to find the perpendicular vector!
Christopher E.
November 22, 2023
calculating the area of the triangle pqr by using the magnitude of pq cross pr divided by two seems like a handy trick the formula he explained makes the calculation straightforward
James P.
December 3, 2023
dylan's explanation about finding the area of the triangle pqr using the cross product method was detailed and easy to follow its useful to understand both finding a vector orthogonal to the plane and calculating the triangles area in 3d space