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Find the lengths of the sides of the triangle $ PQR $. Is it a right triangle? Is it an isosceles triangle?

$ P (3, -2, -3) $ , $ Q (7, 0, 1) $ , $ R (1, 2, 1) $

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Kyle Parsotan

May 12, 2020

explain

Missouri State University

Campbell University

Harvey Mudd College

Baylor University

Lectures

02:56

In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.

11:08

In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.

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feelings of the side of the triangle. We want to figure out whether it's right or ice Australis. All right, so let's find the length between P and Q. This is square root of three minus seven squared, plus native to minus zero squared, plus native three minus one square. Okay, sends up being sixteen plus for plus four. Um, I'm tired plus sixteen here in a CZ thirty six, which is six. Now. Let's find the length between Pienaar. Hey, so that's three nine x one squared, plus negative one. One is two squared, plus native, three minus one squared. Okay, so here will get here. We're going to get four hearing at sixteen, hearing another sixteen. Again. Get swear to thirty six, which is six. There's definitely I saw sleaze. Okay, there's two sides are equal. No need to find the length between Q and our. Okay, Q is seven. Then our is one squared plus zero minus two squared plus. Let's see. And they've got a one minus one squared. Hey, since I'm being square route forty just to read ten, so triangle looks like six. And that another six I got two Rad, huh? Okay, so it is not right, But it is my sausage. It was right. This would be Teo be six, right?

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