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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






                                                                                                                                                                        ------------xxxx------------


                                                                                           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 !





Complete Tutorial (There is an MCQ Quiz after this):





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





In case you're interested in learning more about Vectors, here's the full set of tutorials we have :

Vectors 1a ( Theory and Definitions: Introduction to Vectors; Vector, Scalar and Triple Products)
Introducing a vector, position vectors, direction cosines, different types of vectors, addition and subtraction of vectors. Vector and Scalar products. Scalar Triple product and Vector triple product and their properties. Components and projections of vectors.

Vectors 1b ( Solved Problem Sets: Introduction to Vectors; Vector, Scalar and Triple Products )
Solved examples and problem sets based on the above concepts. 



Vectors 2a ( Theory and Definitions: Vectors and Geometry ) Vectors and geometry. Parametric vectorial equations of lines and planes. Angles between lines and planes. Co-planar and collinear points. Cartesian equations for lines and planes in 3D. 

Vectors 2b ( Solved Problem Sets: Vectors and Geometry )

Solved examples and problem sets based on the above concepts.






Vectors 3a ( Theory and Definitions: Vector Differential and Integral Calculus ) Vector Differential Calculus. Derivative, curves, tangential vectors, vector functions, gradient, directional derivative, divergence and curl of a vector function; important formulas related to div, curl and grad. Vector Integral Calculus. Line integral, independence of path, Green's theorem, divergence theorem of Gauss, green's formulas, Stoke's theorems.


Vectors 3b ( Solved Problem Sets: Vector Differential and Integral Calculus ) - Solved examples and problem sets based on the above concepts.



 

 


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