# Dot product online study

Introduction to dot product online study:

From online, we can get a clear definition for every topic. Online is very useful to study about topics especially for mathematics. Dot product is a mathematical term related to vectors. That is, dot product is one type of product of vectors. Dot product is denoted as a . b for vectors 'a' and 'b'. Let us study the definition of dot product.

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## Explanation to dot product online study:

The general form of dot product for two vectors a = [a1, a2, a3, ..., an] and b = [b1, b2, b3, ..., bn] is as follows.

a . b = `sum_(k=1)^n` akbk

= a1b1 + a2b2 +  a3b3 + ... + anbn

By studying the above online formula for dot product, we can find the dot product of different vectors

## Example problems to dot product online study:

Example: 1

Find out the dot product of vectors a = 3i + 7j and b = 2i + 9j.

Solution:

Given:

a = 3i + 7j

a = (3, 7)

a1 = 3

a2 = 7

b = 2i + 9j

b = (2, 9)

b1 = 2

b2 = 9

Now, the dot product is,

a . b = a1b1 + a2b2

= (3)(2) +(7)(9)

= 6 + 63

= 69

Answer: a . b = 69

Example: 2

Find out the dot product of vectors a = i + 4j + 5k and b = 3i + 7j + 5k

Solution:

Given:

a = i + 4j + 5k

a  = (1, 4, 5)

a1 = 3

a2 = 7

a3 = 5

b = 3i + 7j + 5k

b  = (3, 7, 5)

b1 = 3

b2 = 7

b3 = 5

Now, the dot product is,

a . b = a1b1 + a2b2 + a3b3

= (3)(3) + (7)(5) + (5)(5)

= 9 + 35 + 25

= 69

Answer: a . b = 69

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## Practice problems to dot product online study:

Problem: 1

Find out the dot product of vectors a = [1, 2] and b = [-3, 8]