3D Geometry

• The 3D Geometry section places strong emphasis on understanding vector algebra and its application within the three-dimensional realm.

• Engage with the fundamental concept that vectors can be plotted within three-dimensional space, offering a powerful tool for solving complex geometry problems.

• Recognize that a vector’s direction is usually expressed using three numbers, known as coordinates, exemplifying its position in 3D space.

• Study Cartesian coordinates within 3D geometry. Similar to 2D geometrical spaces, 3D employs three axes - namely, x, y, and z - instead of two, enabling a much richer, deeper understanding of object placement and movement within this realm.

• Learn to calculate using vectors and matrices, understanding their crucial role in various transformations within three-dimensional space.

• Develop an understanding of scalar products, which is a way of multiplying two vectors together to yield a scalar. Note how scalar products can be used to find the angle between two vectors or determine whether vectors are perpendicular.

• Master the concept of vector equation of a line, which links the position vectors of points on the line in a linear relationship. This is of paramount importance in establishing geometric frames of reference within three-dimensional space.

• Develop proficiency in understanding and calculating the vector and cartesian equation of a plane.

• Understand the concept of a line of intersection of two planes, and be able to calculate it.

• Grasp the concept of the angle between two planes and be able to calculate it.

• Review the concept of perpendicular distance from a point to a plane and learn how to calculate it.

• Learn to use scalar triple product. This technique allows you to calculate the volume of a parallelepiped, establish whether three vectors are coplanar and verify the condition for three lines to be concurrent.