Answer:
Follows are the solution to this question:
Step-by-step explanation:
Given:
[tex]P= (3,-4)\\\\Q=(-2,-4)\\\\\overrightarrow{PQ}=?\\\\Magnitude=?\\\\\text{Direction of the vector}=?\\\\[/tex]
Calculating [tex]\overrightarrow{PQ}[/tex]:
[tex]\to \overrightarrow{PQ} = \overrightarrow{Q} -\overrightarrow{P}[/tex]
[tex]= (-2, -4) - (3,-4)\\\\= (-2\ -3, -4 \ -(-4)) \\\\= (-5 ,0)\\\\ = -5i+0j[/tex]
Calculating magnitude:
[tex]\to || \overrightarrow{PQ} || = \sqrt{i^2+j^2}[/tex]
[tex]=\sqrt{-5^2+0^2}\\\\=\sqrt{25+0}\\\\=\sqrt{25}\\\\=5[/tex]
Calculating the direction of the vector:
[tex]\overrightarrow{V} = \frac{\overrightarrow{PQ}}{|| \overrightarrow{PQ}||}[/tex]
[tex]= \frac{5i+0j}{5}\\\\= \frac{5i}{5}\\\\= i[/tex]
