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Vectors in 2D/3D Geometry: Solved Problems,Examples, MCQ Quizzes - Shortest/Perpendicular Distances, Proving properties of Triangles, Tetrahedrons and Parallelograms using Vector methods


                                                                                           Vectors in 2D/3D Geometry

You will learn how to solve problems using vector methods related to the following topics ( There is also an MCQ Quiz/Test after the tutorial):

Finding the distance between 2 lines given their vector equations.

Finding the distance of a point from a plane in 3D.

Finding the vector equation of a plane passing through two planes and a given point.

Finding out whether 2 given lines are coplanar or three given points are collinear.

Finding the vectorial equation of the line of intersection of two planes.

You will see Vector Methods can be used to Prove Geometric Properties such as :

The bisector of an angle in a triangle divides the (opposite) side in the ratio of the length of the 2 sides which form the angle being bisected. 

Six planes through the middle of each point in a tetrahedron and perpendicular to the opposite edge, meet in a point.

A square PQRS is folded along the diagonal such that the planes of the two triangles thus formed are now perpendicular to each other. How do you find the shortest distance between PQ and RS (opposite sides, which are now in 2 different triangles ) ?

If ABCD is a tertahedron, K is the midpoint of AB and L is the midpoint of CD, prove that every line passing through K and L divides the tetrahedron into two parts of equal volume.

.. And other challenging problems !

MCQ Quiz

Companion MCQ Quiz for this tutorial - test how much you know about the topic. Your score will be e-mailed to you at the address you provide.

MCQ Quiz: Vectors & ttheir applications in 2D/3D Geometric Problems

MCQ Quiz #2: Vectors and Geometry
Read the questions in the document below. Fill up your answers in the answer submission form below it. Your score will be emailed to you.

MCQ Quiz #2 (Vectors and Geometry)

Answer Submission Form

Answer Submission Form: MCQ Quiz #2: Vectors and Geometry