#### A PHP Error was encountered

Severity: Warning

Message: count(): Parameter must be an array or an object that implements Countable

Filename: controllers/calculator.php

Line Number: 37

Dot Product Calculator - Online Calculator - Tutorpace

# Dot Product Calculator

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

#### SIGN UP FOR A FREE TRIAL

Dot Product is the product of the magnitudes of the two given vectors. Dot product is also called as Scalar product since the final result is just a scalar number with only magnitude and no direction. Dot product calculator is the online tool which can help us calculate the dot product between two vectors.

Example 1:Given two vectors, a = <2, 1, 3> and b = <-1, 5, 4>

Dot product is given by > a .b = <2, 1, 3>.<-1, 5, 4>

> Since dot product is just a scalar product between numbers, we get

> a.b = (2 * -1) + (1 * 5) + (3 * 4)

> a.b = -2 + 5 + 12

> a.b = 15

Hence the dot product between the given vectors ‘a’ and ‘b’ > a.b = 15

Example 2: Given vector ‘a’ has magnitude of 4 and vector ‘b’ has magnitude of ‘5’.  If the angle between the two vectors is 60°, then find the dot product between them.

Given magnitude of vector ‘a’ > | a | = 4

Given magnitude of vector ‘b’ > | b | = 5

Given angle between vectors ‘a’ and ‘b’ > θ= 60°

Dot Product between vectors ‘a’ and ‘b’  > a.b = | a| * | b | * cosθ

> a.b = 4 * 5 * cos(60°)

> a.b = 20 * ½

> a.b = 10