Scalar Multiplication Calculator

Published on: February 15, 2026
Final Answer: Free • Full Steps: Pro

This Scalar Multiplication Calculator helps you multiply a 3D vector by a scalar. Multiply each component of the vector by the same scalar value, then write the results together as a new vector. This follows the scalar multiplication rule used in coordinate geometry and vector algebra. It is a simple way to check answers, understand the method clearly, and practise vector operations step by step.

Step-by-step method

  1. Identify the scalar and the vector components.
  2. Write the scalar multiplication rule.
  3. Substitute values into the rule.
  4. Multiply each component and simplify.

Formula:

\(k\vec{A} = \left\langle k a_{1},\; k a_{2},\; k a_{3} \right\rangle\)