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]
