Question:

Answer the following as true or false. 
(i)a→and -a→are collinear. 
(ii)Two collinear vectors are always equal in magnitude. 
(iii)Two vectors having same magnitude are collinear. 
(iv)Two collinear vectors having the same magnitude are equal.

Updated On: Sep 1, 2023
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Solution and Explanation

(i)True Vectors a→and -a→are parallel to the same line. 
(ii)False Collinear vectors are those vectors that are parallel to the same line. 
(iii)False.

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Concepts Used:

Types of Vectors

In general, vectors are used in Maths and Science and are categorized into 10 different types of vectors such as:-

  1. Unit Vector - When a vector has a magnitude of 1 unit length, called a Unit Vector.
  2. Co-Initial Vector - Two or more vectors that have the same initial point are known to be Co-Initial Vectors.
  3. Coplanar Vector - Vectors that lie either in the same plane or are parallel to the same plane are called Coplanar vectors.
  4. Equal Vector - When two vectors have equal direction as well as magnitude, they are Equal Vectors, even if the initial point is different for both vectors.
  5. Negative of a Vector - When two vectors have the same magnitude but have exactly different directions.
  6. Zero Vector - When a vector has the same starting and ending point and has zero magnitudes is called a zero vector. The starting point needs to coincide with the terminal point. It is denoted by 0. It is also known as the null vector.
  7. Position Vector - A vector that indicates the location or the position of a point in a plane (three-dimensional Cartesian system) w.r.t. its origin. If A is a reference origin and there’s an arbitrary point B in the plane then AB will be called the position vector of the point.
  8. Like and Unlike Vectors - Like vectors are the vectors that have the same direction. And unlike vectors are the vectors that have opposite directions.
  9. Collinear Vector - Vectors either lying in the same line or which are parallel to the same line are Collinear vectors.
  10. Displacement Vector - The vector AB will be known as a displacement vector if a point is displaced from position B to position A.