Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Prove Properties 2, 4, and 5 of the dot product (Theorem 2).

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Johns Hopkins University

Missouri State University

Harvey Mudd College

Boston College

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.

03:52

Prove Properties $2,4,$ an…

01:35

Prove Property 4 of the do…

The problem is proof properties, 24 and 5 of the dot product property 2 is a dot b, is equal to b dot a here we can let a is equal to a 1 a 2. A 3 point b is equal to e o b 2 b 3. So a dot b is equal to a 1 b 1 plus a 2 b 2 plus a 3 b, 3 and b dot a is equal to v, 1, a 1 plus b 2, a 2 plus 8 e 3 a 3. So this is equal to a 1 b 1 plus a 2 v 2 plus 3 b 3 s. This is equal to a dot b. Property 4 is scattered c times. A dot b is equal to scatter c times. A dot b is equal to a dot square c times b, so first to reprove this equation, and similarly we can prove another equation: a is equal to c a 1 c, a 2 c, a 3 point. So c, a dot b is equal to c, a 1 b, 1 plus c, a 2 b, 2 plus c 83 b 3 point. So this is equal to c times a 1 b, 1 plus a 2 b, 2 plus 83 b 3 point. So this is equal to s times a dot b. To similarly become proof. The other equation- property 5- is 0 dot. A is equal to 00 is a vector, 000 point, so 0 dot a is equal to 0 times a 1 plus 0 times a 2 plus 0 times a 3 point. So this is equal to 0.

View More Answers From This Book

Find Another Textbook

02:16

number of four digit numbers with all digits different and containing the di…

02:08

P is point out side the circle. If the farthest distance of P from the circl…

00:56

The dimensions of a cuboidal iron slab are 1.5m × 25cm × 150cm . Find its vo…

05:57

The height of a hill is 3,300 metres. From the point D on the ground the ang…

03:06

A box contains 5 radio tubes of which 2 are defective.The tubes are tested o…