# Vector Scalar Multiplication Calculator

## Multiply vectors by a scalar step by step

The calculator will multiply the given vector by the given scalar, with steps shown. It handles vectors of any size.

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If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Our calculator for vector scalar multiplication offers a fast, reliable, and effective solution for computing the product of a vector and a scalar. The resultant vector is immediately presented, bolstering your grasp of the concept and affirming the correctness of your calculations.

## How to Use the Vector Scalar Multiplication Calculator?

• ### Enter the Vector

Input the coordinates of the vector in the given fields. The calculator can handle both 2D and 3D vectors.

• ### Enter the Scalar

Type in the scalar value by which you want to multiply the vector.

• ### Calculate

Click on the "Calculate" button to execute the vector scalar multiplication.

• ### Result

The resulting vector is displayed instantly.

## Understanding Vector Scalar Multiplication

Vector scalar multiplication involves multiplying a vector by a scalar (a single number). The result of the vector scalar multiplication is a new vector where each coordinate of the original vector is multiplied by the scalar.

If you have a vector $\mathbf{\vec{u}}=\langle u_1,u_2\rangle$ and you multiply it by a scalar $c$, the formula for the vector scalar multiplication is

$$c\mathbf{\vec{u}}=\langle cu_1,cu_2\rangle$$

In the case of a 3D vector, if $\mathbf{\vec{v}}=\langle v_1,v_2,v_3\rangle$, the result of the vector scalar multiplication will be

$$c\mathbf{\vec{v}}=\langle cv_1,cv_2,cv_3\rangle$$

## Example of Vector Scalar Multiplication

Let's say we have a vector $\mathbf{\vec{v}}=\langle 2,3,4\rangle$ and we want to multiply it by a scalar $3$. Using our vector scalar multiplication calculator, we can easily compute this:

$$3\cdot\langle 2,3,4\rangle=\langle 3\cdot 2,3\cdot 3,3\cdot 4\rangle=\langle 6,9,12\rangle$$

The resulting vector is $\langle 6,9,12\rangle$.

## Why Choose Our Vector Scalar Multiplication Calculator?

• ### Efficiency

Our calculator performs quick and precise calculations, saving you time and effort in solving complex vector scalar multiplication problems.

• ### Accuracy

The calculator ensures accurate results, removing the chance of errors that can occur with manual calculations.

• ### Ease of Use

The user-friendly interface makes it easy for anyone to input the values and get results instantly. No advanced technical skills required.

• ### Understand Concepts Better

With immediate results, you can solidify your understanding of vector scalar multiplication, learning how changes in vectors and scalars affect the resulting vector.

• ### Supports Both 2D and 3D vectors

The calculator is capable of handling both 2D and 3D vectors, providing a versatile tool for various mathematical computations.

### FAQ

#### What is the formula for vector scalar multiplication?

For a 2D vector $\mathbf{\vec{u}}=\langle u_1,u_2\rangle$ and a scalar $c$, the formula is $c\mathbf{\vec{u}}=\langle cu_1,cu_2\rangle$. For a 3D vector $\mathbf{\vec{v}}=\langle v_1,v_2,v_3\rangle$, the formula is $c\mathbf{\vec{v}}=\langle cv_1,cv_2,cv_3\rangle$.

#### Does multiplying a vector by a scalar change its direction?

Multiplying a vector by a positive scalar changes its magnitude (if the scalar doesn't equal $1$) but not its direction. If multiplied by a negative scalar, the resulting vector will have a different magnitude (if the scalar doesn't equal $-1$) and an opposite direction.

#### What is vector scalar multiplication?

Vector scalar multiplication is a mathematical operation where each coordinate of a vector is multiplied by a scalar (a single real or complex number). The result is a new vector.