Chapter 9: Q. 2 (page 612)

If $v = a_{1} i + b_{1} j$ and $w = a_{2} i + b_{2} j$ are two vectors, the ____ is defined as $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$ .

Short Answer

Expert verified

If $v = a_{1} i + b_{1} j$ and $w = a_{2} i + b_{2} j$ are two vectors, theDot Product is defined as $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$ .

Step by step solution

Step 1. Given Information

We are given an incomplete statement about the dot product.

We have to complete the given statement

Step 2. Completing the Statement

The product of uand v is the dot product.

It is because dot product between two vectors always produces a scalar.

The complete statement is,

If $v = a_{1} i + b_{1} j$ and $w = a_{2} i + b_{2} j$ are two vectors, the Dot Product is defined as $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

If $v = a_{1} i + b_{1} j$ and $w = a_{2} i + b_{2} j$ are two vectors, the ____ is defined as $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$ .

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Completing the Statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If v=a1i+b1jandw=a2i+b2j are two vectors, the ____ is defined as v·w=a1a2+b1b2.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Completing the Statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Discrete Mathematics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

If $v = a_{1} i + b_{1} j$ and $w = a_{2} i + b_{2} j$ are two vectors, the ____ is defined as $v \cdot w = a_{1} a_{2} + b_{1} b_{2}$ .