Introduction to i and j Vectors

Introduction to i and j Vectors

Basics of Vectors

• Vectors are quantities with both magnitude (size) and direction.
• They can be represented as a directed line segment.
• The length of the vector represents its magnitude, while the arrow denotes the direction.

Vector Algebra

• Vectors can be added or subtracted using triangle law or parallelogram law of vectors.
• Scalar multiplication is multiplying a scalar quantity with a vector which affects its magnitude but not its direction.
• The zero vector (also known as null vector) has zero magnitude and is directionless.

Position Vectors

• A position vector points from the origin to the point in space.
• The negative of a vector has the same magnitude but opposite direction.

Units of Vectors

• The basis i and j unit vectors are used to represent vectors in the 2D plane.
• i represents a unit vector in the x-direction and j represents a unit vector in the y-direction.
• A vector can be broken down into its i and j components.

Vector Equations

• We can equate vectors to solve for unknowns, create equations, or deduce relations.
• For equality, vectors must have the same magnitude and direction.

Scalar and Vector Products

• The dot product (scalar product) of two vectors results in a scalar.
• The cross product (vector product) of two vectors results in a vector.

Applications of Vectors

• Vectors have extensive applications in physics, engineering, computer graphics, and navigational systems.
• Knowing how to manipulate vectors is crucial for solving real-world problems.