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Use vectors to decide whether the triangle with vertices $ P (1, -3, -2) $, $ Q (2, 0, -4) $, and $ R (6, -2, -5) $, is right-angled.

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Brandon B.

January 18, 2022

I checked this answer on other resources, they say it is right-angled. When I did the math I found a vector to be zero

Harvey Mudd College

Baylor University

University of Nottingham

Idaho State 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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04:30

Okay, so we want to figure out if this is a right angled triangles. So we need to take the dot product between each one of these. So the dot product between P and Q is going to be two times one. That's negative. Three times zero. It's negative. Two times negative. Four. Okay, After we do this, we get negative. Six. So remember, if the dot product is zero, then we have a right angle, so we don't have a right angle yet. Let's do P and R. So we've got one time. Six plus negative. Three times negative. Two plus negative. Two times negative. Five. Okay, so here we're going to end up with six plus six, which is 12 plus 10, which is 22. So again, still no. Um, right angle. So let's take the dot product between p Sorry, Q and R. So we got two times six plus zero times negative two and then plus negative four times negative five. Yeah, And again, we end up with 12. Plus, uh, I'm sorry. 12 plus 20. Just 2022. So no right angle. So this is no

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