MathsCoplanar Vectors – Explanation, Conditions and FAQs

Coplanar Vectors – Explanation, Conditions and FAQs

Coplanar Vectors Introduction

A coplanar vector is a vector that is located in the same plane as another vector. This is often done for convenience when working with vectors, as it makes calculations and manipulations simpler. In physics, a vector is a mathematical representation of a physical quantity, such as force or momentum. Vectors can be added, subtracted, and multiplied together, and they have a direction and a magnitude.

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    All about Coplanar Vectors

    A coplanar vector is a vector that lies in the same plane as another vector. In other words, the two vectors are parallel to each other. This can be easily visualized using a two-dimensional plane. If two vectors are drawn on the plane, and they lie in the same line, then they are coplanar vectors.

    The magnitude of a coplanar vector is simply the sum of the magnitudes of the individual vectors. The direction of a coplanar vector is the same as the direction of the individual vectors.

    Coplanar vectors are often used in physics and engineering. For example, they can be used to model the forces between objects.

    Equality of Vectors

    Two vectors are said to be equal if they have the same magnitude and direction.

    Types of Vectors

    There are three types of vectors: magnitude, direction, and displacement vectors.

    A magnitude vector is simply the magnitude (or size) of a vector. It has no direction information.

    A direction vector has both magnitude and direction information. It points in a specific direction.

    A displacement vector has magnitude and direction information, and it also has a starting point and an ending point. It shows the displacement between the two points.

    Coplanarity in Theory and Practice

    Theory

    In theory, coplanarity is the condition of being on the same plane. This means that all of the features on a part are at the same height and that there are no gaps or overlaps between them.

    Practice

    In practice, coplanarity is often difficult to achieve. This is because it is often difficult to measure and to maintain the same height across a variety of features. Even slight variations can cause problems with fit and assembly.

    Conditions for Coplanar Vectors/ Properties of Coplanar Vectors

    Two vectors are said to be coplanar if they lie in the same plane.

    If vectors A and B are coplanar, then they have the following properties:

    • Their sum is a vector in the same plane as A and B.

    • Their difference is a vector in the same plane as A and B.

    • Their product is a vector in the same plane as A and B.

    What are Linearly Independent Vectors?

    Linearly independent vectors are vectors that can be written as a linear combination of each other, but not all linear combinations of vectors are independent.

    What are Linearly Dependent Vectors?

    Linearly dependent vectors are vectors that are related to each other in a way that one vector can be expressed as a combination of the other vectors.

    How do you Know if Two Vectors are Coplanar?

    If two vectors are coplanar, then they will have the same orientation and lie in the same plane.

     

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