Question

Consider two vectors $A = 3i - 1j$ and $B = - i - 5j$, how do you calculate $A - B$?

Answer 1

Answer of will $A - B$ be simply substituting the values, regrouping the like terms and performing the subtraction operation between the two.

Complete step by step answer:
This is a simple question of vector addition.
Here, it is given that and and we are supposed to find
For doing this, we just need to put values of these two vectors and subtract the like terms. Like terms in this case would be the ones having i and j
So,
$A - B = \left( {3i - 1j} \right) - \left( { - i - 5j} \right)$
Opening the brackets we will get (remember there is a negative sign before the bracket)
$\Rightarrow \left( {3i - 1j} \right) + i + 5j$
Regrouping and putting the like terms together we will get
$\Rightarrow 3i - 1j + i + 5j$
Rearranging the terms we will get
$\Rightarrow 3i + i - 1j + 5j$
Taking I and j common we will get
$\Rightarrow i\left( {3 + 1} \right) - j\left( { - 1 + 5} \right)$
Further simplifying we will get
$\Rightarrow 4i - 4j$
Hence
$A - B = 4i - 4j$

Note: Scalar quantity is defined as the physical quantity with magnitude and no direction.
Some physical quantities can be described just by their numerical value (with their respective units) without directions (they don’t have any direction).
The addition of these physical quantities follows the simple rules of the algebra. Here, only their magnitudes are added.
Examples of Scalar Quantities
There are plenty of scalar quantity examples, some of the common examples are:
Mass, Speed, Distance, Time, Area, Volume, Density, Temperature etc.
Vector Quantity-
A vector quantity is defined as the physical quantity that has both direction as well as magnitude.
A vector with the value of magnitude equal to one and direction is called a unit vector represented by a lowercase alphabet with a “hat” circumflex. That is “û“.
Examples of Vector Quantities
Vector quantity examples are many, some of them are given below:
Linear momentum, Acceleration, Displacement, Momentum, Angular velocity, Force, Electric field, Polarization etc.