Repeated addition of a Vector
» Repeated addition is generalized to Multiplication of a vector by Scalar
» Components are multiplied by scalar
We have learned about addition of two or more vectors. Consider a vector that is added to itself. The result of the addition is ' '. If then . This equals .
Repeated addition can be generalized to multiplication of vector by a scalar. Scalar multiplier is denoted with to identify differently to the component values . Note that the scalar multiplier and component values are real numbers.
The result of is ''.
Can a vector be divided by a real number ?
Yes. Division is inverse of multiplication.
If the given vector is then
`quad quad = a/lambda i+b/lambda j+c/lambda k
Multiplication of Vector by a scalar: For any vector and scalar
When vector is multiplied by a scalar, the vector scales up or down proportionally.
The outline of material to learn vector-algebra is as follows.
Note: Click here for detailed outline of vector-algebra.
• Introduction to Vectors
→ Introducing Vectors
→ Representation of Vectors
• Basic Properties of Vectors
→ Magnitude of Vectors
→ Types of Vectors
→ Properties of Magnitude
• Vectors & Coordinate Geometry
→ Vectors & Coordinate Geometry
→ Position Vector of a point
→ Directional Cosine
• Role of Direction in Vector Arithmetics
→ Vector Arithmetics
→ Understanding Direction of Vectors
• Vector Addition
→ Vector Additin : First Principles
→ Vector Addition : Component Form
→ Triangular Law
→ Parallelogram Law
• Multiplication of Vector by Scalar
→ Scalar Multiplication
→ Standard Unit Vectors
→ Vector as Sum of Vectors
→ Vector Component Form
• Vector Dot Product
→ Introduction to Vector Multiplication
→ Dot Product : First Principles
→ Dot Product : Projection Form
→ Dot Product : Component Form
→ Dot Product With Direction
• Vector Cross Product
→ Vector Multiplication : Cross Product
→ Cross Product : First Principles
→ Cross Product : Area of Parallelogram
→ Cross Product : Component Form
→ Cross Product : Direction Removed