What is a Vector?

A vector is a quantity that has both magnitude and direction. In physics, vectors are used to represent physical quantities such as displacement, velocity, acceleration, and force. Vectors are usually represented graphically as arrows, where the length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector.

Composition of Vectors

When two or more vectors act on a point, their combined effect is known as the resultant vector. To find the magnitude and direction of the resultant vector, we can use the methods of vector addition.

Vector Addition

Vector addition involves adding the components of two or more vectors to find the components of the resultant vector. The magnitude of the resultant vector can be calculated using the Pythagorean theorem, and the direction of the resultant vector can be determined using trigonometric functions such as sine and cosine.

Example

For example, if a car travels east at 60 km/h and then turns north and travels at 40 km/h, we can find the resultant velocity of the car by adding the two velocity vectors. The magnitude of the resultant velocity can be calculated using the formula sqrt((60^2) + (40^2)), and the direction of the resultant velocity can be determined using trigonometry.

In conclusion, vectors are an essential concept in physics that allows us to represent physical quantities with both magnitude and direction. By understanding how to add vectors, we can find the resultant of multiple vectors acting at a point.