Dot product calculator # dotproductcalculator

Dot product calculator solves the scalar values of two vectors in two dimensions or 2d space with step by step worksheet.
Use formula of dot product to solve dot matrix

### Sample 1

Vector a(-5 8 2) and b(6 6 10) , follow these steps:

### Step 1: Entering the values for vector a

Enter as [-5, 8, 2] follow by comma

Enter [6,6,10]

### result

Hit the check mark to solve dot product

### How to Use Dot Product Calculator

Find the dot product of vector a (2, 3, 4) and b (5. 7, 9) using the calculator

• Enter number "2" into the box marked "a1"

• Enter number "3" into the box marked "a2"

• Enter number "4" into the box marked "a3"

• Enter number "5" into the box marked "b1"

• Enter number "7" into the box marked "b2"

• Enter number "9" into the box marked "b3"

• Hit the check mark to solve the dot matrix problem

### What is Dot Product

The dot product, also known as the scalar product, is a mathematical operation performed on two vectors. It results in a scalar value that represents the magnitude of the projection of one vector onto the other vector.

### How to Solve Dot Product of Two Vectors

To solve the dot product of two vectors, follow these steps:

• 1. Write down the two vectors you want to find the dot product of. For example, let's say we have vector A = [a1, a2, a3] and vector B = [b1, b2, b3].

• 2. Multiply the corresponding components of the two vectors together. In other words, multiply a1 by b1, a2 by b2, and a3 by b3.

• 3. Add up the results from step 2. For example, if the results from step 2 are c1, c2, and c3, then the dot product is c1 + c2 + c3.

• 4. Write down the dot product as a scalar value.

#### Example 1

Let A = [2, 3, 4] and B = [1, -2, 5].

Multiply the corresponding components:

• a1 x b1 = 2 x 1 = 2

• a2 x b2 = 3 x -2 = -6

• a3 x b3 = 4 x 5 = 20

• 2 + (-6) + 20 = 16

So, the dot product of vectors A and B is 16.

### Solving The Dot Product of Three Vectors.

To find the dot product of three vectors, you need to perform the dot product operation twice.

Let's say we have three vectors: A = [a1, a2, a3], B = [b1, b2, b3], and C = [c1, c2, c3].

• Step 1. First, find the dot product of vectors A and B:
A · B = (a1 * b1) + (a2 * b2) + (a3 * b3).

• Step 2. Then, find the dot product of the result from step 1 with vector C:
(A · B) · C = [(a1 * b1) + (a2 * b2) + (a3 * b3)] · C = (a1 * b1 * c1) + (a2 * b2 * c2) + (a3 * b3 * c3).

• Let A = [2, 3, 1], B = [4, -1, 5], and C = [-2, 0, 3].

• 1. Find the dot product of vectors A and B:
A · B = (2 * 4) + (3 * -1) + (1 * 5) = 8 - 3 + 5 = 10.

• 2. Find the dot product of the result from step 1 with vector C:
(A · B) · C = 10 · C = (10 * -2) + (10 * 0) + (10 * 3) = -20 + 0 + 30 = 10.

Therefore, the dot product of the three vectors A, B, and C is 10.

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