Concept of a Vector

Concept of a Vector

Fundamentals of Vectors

• Vectors represent a quantity that has both magnitude and direction.

• A vector can be drawn as an arrow. The length of the arrow represents the magnitude, and the direction of the arrow represents the direction of the vector.

• Vectors are usually denoted by bold lowercase letters like a or b.

Representing Vectors

• Vectors in two-dimensional space are often represented as an ordered pair (x, y).

• In three-dimensional space, they are represented as an ordered triple (x, y, z).

• These numbers tell you how far to go in the horizontal, vertical, and (if applicable) out-of-page directions.

Mathematical Operations with Vectors

• Adding vectors involves adding corresponding components. If a = (a1, a2) and b = (b1, b2), then a + b = (a1 + b1, a2 + b2).

• Scalar multiplication: when a vector is multiplied by a number (scalar), each component of the vector is multiplied by that number.

• The dot product of two vectors is computed by multiplying corresponding elements and then adding those products.

Applications of Vectors

• Vectors are fundamental in physics; they’re used to represent quantities like force and velocity.

• Vectors in computer graphics are used to represent the movement of objects.

• They’re also used in calculus and other branches of mathematics to study functions with multiple variables.

Remember, vectors are an essential tool in expressing both direction and magnitude. Grasping their basic concepts and operations is crucial for more advanced maths and physics topics.