Multiplication of Vectors with Scalar
Multiplying a vector a with a constant scalar k gives a vector whose direction is the same but the magnitude is changed by a factor of k.
The figure shows the vector after and before it is multiplied by the constant k. In mathematical terms, this can be rewritten as,
[Tex]|k\vec{a}|~=~k|\vec{a}| [/Tex]
if k > 1, the magnitude of the vector increase while it decreases when the k < 1. The image added below shows the scaler multiplication of vec a with a scaler number k where k is any constant greater than 1. (k>1)
Vector Operations
Vector Operations are operations that are performed on vector quantities. Vector quantities are the quantities that have both magnitude and direction. So performing mathematical operations on them directly is not possible. So we have special operations that work only with vector quantities and hence the name, vector operations.
Thus, It is essential to know what kind of operations can be performed on the vector quantities and vector operations tells us about the same. This article deals with vector operations, such as vector addition, the cross product of two vectors, the dot product of two vectors, and others in detail. Let’s learn about all of them in detail, here in this article.
Table of Content
- Operations on Vectors
- Addition of Vectors
- Triangle Law of Vector Addition
- Parallelogram Law of Vector Addition
- Subtraction of Two Vectors
- Multiplication of Vectors with Scalar
- Product of Two Vectors
- Dot Product Or Scalar Product of Vector
- Vector Product Or Cross Product of Vectors
- Problems on Vector Operations