Explanation Given Information: The vectors are, v = − 2 i + j And w = 4 i − 3 j . Formula used: The Dot product of two vectors states that, If v = a 1 i + b 1 j and w = a 2 i + b 2 j are vectors, the dot product v ⋅ w is define as, v ⋅ w = a 1 a 2 + b 1 b 2 . The dot product of two vectors is the sum of products of their horizontal components and their vertical components. The angle between two vectors states that, If v = a 1 i + b 1 j and w = a 2 i + b 2 j are vectors, Then, cos θ = v ⋅ w ‖ v ‖ ‖ w ‖ and θ = cos − 1 ( v ⋅ w ‖ v ‖ ‖ w ‖ ) . Where, magnitudes of vectors are: ‖ v ‖ = a 1 2 + b 1 2 And ‖ w ‖ = a 2 2 + b 2 2 . Calculation: Considered the vectors, v = − 2 i + j And w = 4 i − 3 j Now, use dot product formula v ⋅ w = a 1 a 2 + b 1 b 2 : v ⋅ w = ( − 2 ) ( 4 ) + ( 1 ) ( − 3 ) = − 8 − 3 = − 11 Thus, the dot product of two vectors v ⋅ w is − 11

6th Edition

ISBN: 9780134469140

Author: Robert F. Blitzer

Publisher: PEARSON

See similar textbooks

Question

Chapter 11, Problem 21CRE

To determine

To calculate: The dot product of v⋅w and the angle between v and w, where v=−2i+j and w=4i−3j.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 20CRE

Chapter 11, Problem 22CRE

Students have asked these similar questions

The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1. Select all that apply: ☐ f(x) is not continuous at x = 1 because it is not defined at x = 1. ☐ f(x) is not continuous at x = 1 because lim f(x) does not exist. x+1 ☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1). x+→1 ☐ f(x) is continuous at x = 1.

a is done please show b

A homeware company has been approached to manufacture a cake tin in the shape of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the games launch. The base of the cake tin has a characteristic dimension / and is illustrated in Figure 1 below, you should assume the top and bottom of the shape can be represented by semi-circles. The vertical sides of the cake tin have a height of h. As the company's resident mathematician, you need to find the values of r and h that minimise the internal surface area of the cake tin given that the volume of the tin is Vfixed- 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and his 2(+1)²h V = 2

Chapter 11 Solutions

Precalculus (6th Edition)

Ch. 11.1 - Check Point 1 Find: . Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 5CP Ch. 11.1 - Prob. 1CVC Ch. 11.1 - Prob. 2CVC Ch. 11.1 - Prob. 3CVC Ch. 11.1 - Fill in each blank so that the resulting statement...Ch. 11.1 - Fill in each blank so that the resulting statement...

Knowledge Booster

The dot product of v ⋅ w and the angle between v and w , where v = − 2 i + j and w = 4 i − 3 j .

Solution Summary: The author calculates the dot product of vcdot w and the angle between two vectors.

To calculate: The dot product of v⋅w and the angle between v and w, where v=−2i+j and w=4i−3j.

Want to see the full answer?

Chapter 11 Solutions