Properties of Vectors: FAQs

How to calculate difference of two vectors ?

Difference of two vectors is similar to addition and follows the same laws. It can be seen as the addition of the first vector and the negative of the second vector.

How to calculate Area of parallelogram from vector product ?

The Area parallelogram can be found by calculating the magnitude of Vector product of the two given vectors.

How is the direction of cross product determined ?

Direction of the vector product can be determined from the right hand thumb rule , where the thumb points in the direction of the resultant vector when the fingers curl from the first vector to the second vector.

Can vectors with different units be added or subtracted ?

No , vectors with different units can’t be added or subtracted. They must have the same units or dimensions.

Why the dot product of orthogonal vector zero ?

Angle between two orthogonal vectors is 90° and cos90° is zero , so dot product of orthogonal vectors is zero.



Properties of Vectors

Vectors are one of the most important concepts in mathematics. Vectors are quantities that have both magnitude and direction. A vector quantity is represented by an arrow above its head. Vectors help us understand the behaviour of directional quantities in 2D and 3D planes. Vectors are also used for determining the position and change of position of points.

Every vector follows a certain set of rules, known as the properties of vectors. It is highly important to know these properties to have a strong command of vector algebra. In this article, we will see the definition of a vector, the properties of vectors, and the properties of vector products.



Table of Content

  • What is a Vector?
  • Basic Properties of Vectors
    • Components of a Vector
    • Magnitude of a Vector
    • Direction of a Vector
  • Operations on Vectors
    • Addition of Vectors
    • Subtraction of Vectors
    • Scalar Multiplication
    • Equality of Vector
  • Advanced Properties of Vectors
    • Dot Product
    • Cross Product
      • Properties of Vector Product of Vectors
  • Applications of Vectors

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