Given [tex]v = \langle 6, 3 \rangle[/tex] and [tex]w = \langle 1, -2 \rangle[/tex], what is the result of [tex]v - w[/tex]?

A. [tex]\langle 7, 1 \rangle[/tex]
B. [tex]\langle 5, 1 \rangle[/tex]
C. [tex]\langle 5, 5 \rangle[/tex]
D. [tex]\langle 7, 5 \rangle[/tex]



Answer :

To find the result of the vector subtraction [tex]\( v - w \)[/tex], let's break down the process step by step.

Given the vectors:
[tex]\[ v = \langle 6, 3 \rangle \][/tex]
[tex]\[ w = \langle 1, -2 \rangle \][/tex]

The operation [tex]\( v - w \)[/tex] denotes the vector subtraction. Vector subtraction is performed component-wise, which means we subtract the corresponding components of [tex]\( w \)[/tex] from [tex]\( v \)[/tex].

Let's find the individual components of the resulting vector:

1. Subtract the x-components:
[tex]\[ 6 - 1 = 5 \][/tex]

2. Subtract the y-components:
[tex]\[ 3 - (-2) = 3 + 2 = 5 \][/tex]

So, the resulting vector [tex]\( v - w \)[/tex] is:
[tex]\[ \langle 5, 5 \rangle \][/tex]

Therefore, the result of [tex]\( v - w \)[/tex] is:
[tex]\[ \langle 5, 5 \rangle \][/tex]

Among the given choices, the correct answer is:
[tex]\[ \langle 5, 5 \rangle \][/tex]