What is a Vector?

Contents

Do you know what vector is? Why it matters?

It is a paradigm with two properties: magnitude and direction, It designates the mathematical or geometrical depiction. The ability of the vector to represent the direction and magnitude is very sturdy.

Vector is usually drawn as an arrow, its direction is forthwith visible and its length represents its magnitude a vector is written as a letter with a right-handed arrow placed over the letter like  a⃗ .

In order to comprehend vectors, you should know what scalars is. It is a quantity with a magnitude that can be described by a single element of a number field such as a real number, often accompanied by units of measurement eg, cm. It defines a vector space.

A distinctive feature of the vector is that they don’t change their perspectives and remain invariant to the coordinate system. Vector and scalar share this coordinate invariance property. All qualities with these properties are members of the group is called Tensors which are simply mathematical objects that can be used to describe physical properties, just like scalars and vectors. In fact, tensors are merely a generalization of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first-rank tensor.

Now let’s see some types of the vector

• Co-initial vectors is when two or more vectors having the same initial point.
• Two or more vectors parallel to the same line irrespective of their magnitudes and directions are called Collinear vector.
• If two vectors are having the same magnitude and direction regardless of the position of their initial points then it’s called equal vectors.
• Free vectors are parallel displacement of a vector that doesn’t change its magnitude and direction.
• The negative of a vector is when it has the same magnitude with a contrasting direction. i.e negative of CD vector is DC

Can you find the sum or difference of vectors?

Consider the Parallelogram law of vector addition, now

• have 2 vectors a and b
• move vector b parallel to its position such that its initial point coincides with the initial point of vector a
• draw 2 lines parallel to vectors a and b to form a parallelogram
• the resulting diagonal represents the sum of 2 vectors.

You will receive a consistent result even when you apply the Triangle law of vector addition. Similarly, the difference between two vectors is defined as the sum of vector a and negative of vector b. Some of the examples of vectors are velocity, acceleration, force, etc.

There is copious information about vectors, so stay curious.

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