Vector Definition

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In physics, a physical quantity is classified as a scalar or as a vector. A scalar is a quantity which only has magnitude. But a vector is a physical quantity which has both magnitude and direction. A vector is usually represented by the arrow symbol and it becomes very important to keep a check on the direction because of which the quantity is expressed either as a positive sign or as a negative sign. Examples of vectors in physics are displacement, velocity, force etc.
Example 1:   An object is pushed with a force of 45N towards the right direction. A force of 20N is applied on the same object but towards the left direction. What is the resultant or net force acting on the object?

Given: Force applied towards right direction = 45N
Force applied towards left direction = 20N
Let right direction be represented as +45N and left direction be represented as -20N.
Hence, net force = 45 – 20 = +25N

This implies that the net force applied on the object is of 25N towards right direction!

Example 2: Jack walked 5m towards north and 12m down south. Determine Jack’s resulting displacement?

Given: Displacement of Jack in north (or upward) direction = 5m
Displacement of Jack in south (or downward) direction = 12m
Let upward direction be represented as +5m and downward direction be represented as -12m.
Hence, resulting displacement = 5m – 12m = -7m

This implies that the resulting displacement of Jack is 7m down south!

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