Solution
Step 1:
The magnitude of a vector is the length of the vector itself.
Given a bi-dimensional vector, the magnitude of the vector is given by:
[tex]\text{v = }\sqrt{v_x^2+v_y^2}[/tex]Step 2:
where
Vx is the x-component of the vector
Vy is the y-component of the vector
Step 3:
The vector in the problem is ( 7 , -5 )
Where
[tex]\begin{gathered} v_x\text{ = 7} \\ v_y\text{ = -5} \end{gathered}[/tex]Step 4:
[tex]\begin{gathered} \text{v = }\sqrt{7^2\text{ + \lparen-5\rparen}^2} \\ \text{v = }\sqrt{49\text{ + 25}} \\ \text{v = }\sqrt{74} \\ \end{gathered}[/tex]Final answer
[tex]\begin{gathered} Magnitude\text{ of the vector is} \\ \sqrt{74}\text{ or 8.6} \end{gathered}[/tex]