Question

How do you find u + v and u - v given u = i + j and v = 2i - 3j?

Answer 1

Hint: In the given question, we have been asked to find the value of ‘u + v’ and ‘u – v’ and it is given that the value of ‘u’ is equals to i + j and the value of ‘v’ is equal to 2i - 3j. In order to summing and subtracting, we just need to add and subtract the values in a way we solve adding or subtracting of two general equations.

Complete step-by-step solution:
We have given that,
\[u=i+j\] And \[v=2i-3j\]
Now,
\[\Rightarrow u+v=\left( i+j \right)+\left( 2i-3j \right)\]
Simplifying the above expression, we get
\[\Rightarrow u+v=i+j+2i-3j\]
Combining the like terms of the above expression, we get
\[\Rightarrow u+v=3i-2j\]
Thus,
Therefore, the summation of \[u=i+j\] and \[v=2i-3j\] is equal to\[3i-2j\].
Now,
\[\Rightarrow u-v=\left( i+j \right)-\left( 2i-3j \right)\]
Simplifying the above expression, we get
\[\Rightarrow u-v=i+j-2i+3j\]
Combining the like terms of the above expression, we get
\[\Rightarrow u-v=-i+4j\]
Thus,
Therefore, the subtraction of \[u=i+j\] and \[v=2i-3j\] is equal to\[-i+4j\].
Hence, it is the required answer.

Note: While solving these types of questions students need to be very careful while writing down the terms of the given expressions and always make sure you are performing the mathematical operations such as addition and subtraction very explicitly to avoid making errors. You should avoid any type of calculation mistakes. We need to subtract and add a given expression in a way we add and subtract numbers and then we just need to combine the like terms and we will get our required answer.