On this page we will discuss vectors in two dimensions for Grade 11 Physical Sciences learners. We have included the notes on pdf format, as well as questions and answers.
In grade 11 Physical Sciences, vectors in two dimensions are a critical concept to understand. Here is a summary of the key points covered in the lesson on vectors in two dimensions:
- Definition of a Vector: A vector is a quantity that has both magnitude and direction. It is represented by an arrow, with the length of the arrow representing the magnitude of the vector and the direction of the arrow representing the direction of the vector.
- Addition of Vectors: Vectors can be added together to find the resultant vector. This is done by placing the tail of one vector at the head of the other and drawing a new arrow from the tail of the first vector to the head of the second. The magnitude and direction of the new arrow (resultant vector) are determined by the tip-to-tail method.
- Subtraction of Vectors: Vectors can also be subtracted from each other. To do this, reverse the direction of the vector that is being subtracted and then add it to the other vector.
- Scalar Multiplication: A scalar is a number that is used to multiply a vector. When a vector is multiplied by a scalar, its magnitude changes, but its direction remains the same.
- Components of Vectors: A vector can be represented by its components, which are the horizontal and vertical components of the vector. These components can be found using trigonometry.
- Unit Vectors: A unit vector is a vector with a magnitude of 1. It can be used to represent the direction of a vector without considering its magnitude.
- Vector Projections: A vector projection is the projection of one vector onto another vector. This is a useful concept for understanding the relationship between two vectors.
These are some of the key points covered in the lesson on vectors in two dimensions in grade 11 Physical Sciences. Understanding these concepts is important for further study in physics and engineering.
Understanding Vectors in Two Dimensions
A vector is a mathematical quantity that has a magnitude and a direction. Vectors can be either two dimensional, with components in the x and y directions, or three-dimensional, with components in the x, y, and z directions.
Vectors in Two Dimensions Grade 11 Popular Questions
- A forward horizontal force of 50 N is applied to a crate. A second horizontal force of 180 N is applied to the crate in the opposite direction. Determine the magnitude and direction of the resultant force acting on the crate.
- The athlete at point A runs 150 m east, then 70 m west and then 100 m east. Determine the resultant displacement of the athlete relative to point A.
- Three forces act on an object in the vertical plane. Two forces of 500 N and 300 N act vertically upwards and the third force of 600 N acts vertically downwards. Determine the resultant force acting on the object.
- An aircraft flies 8 km north from an airport and then 12 km east.
- Use the tail-to-head method to draw a neat labelled displacement vector diagram. Draw in the resultant displacement vector.
- Determine the magnitude and direction of the resultant displacement of the aircraft relative to the airport.
- A drone at point P is flown 2 km north, then 5 km east and then 8 km south. Find the magnitude and direction of the resultant displacement of the drone from point P. Draw a neat labelled displacement vector diagram to support your calculation.
View answers from the pdf document HERE