Practice Math With Us

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.


Please express your views of this topic Dot Product of Parallel Vectors  by commenting on blog. 


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


Between, if you have problem on these topics Define Derivatives ,please browse expert math related websites for more help on  Fraction Simplifier.


Practice problems to dot product online study:


Problem: 1

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

Answer: 13

Problem: 2

Find out the dot product of vectors a = [7, 9] and b = [3, 2]

Answer: 39