**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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The general form of dot product for two vectors a = [a_{1}, a_{2}, a_{3, }..., a_{n}] and b = [b_{1}, b_{2}, b_{3}, ..., bn] is as follows.

a . b = `sum_(k=1)^n` a_{k}b_{k}

= a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3} + ... + a_{n}b_{n}

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

**Example: 1**

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

**Solution:**

Given:

a = 3i + 7j

a = (3, 7)

a_{1} = 3

a_{2} = 7

b = 2i + 9j

b = (2, 9)

b_{1} = 2

b_{2} = 9

Now, the dot product is,

a . b = a_{1}b_{1} + a_{2}b_{2}

= (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)

a_{1} = 3

a_{2} = 7

a_{3} = 5

b = 3i + 7j + 5k

b = (3, 7, 5)

b_{1} = 3

b_{2} = 7

b_{3} = 5

Now, the dot product is,

a . b = a_{1}b_{1} + a_{2}b_{2} + a_{3}b_{3}

= (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.

**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