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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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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.