ANSWER
[tex]|v| = 2 \sqrt{10} [/tex]
EXPLANATION
Vector v that has an initial point of (1,3) and a terminal point of (7,1)
To find vector v, subtract the terminal position vector from the initial position vector.
[tex]v = \binom{7}{1} - \binom{1}{3} [/tex]
[tex]v = \binom{7 - 1}{1 - 3} [/tex]
[tex]v = \binom{6}{ - 2} [/tex]
The magnitude of the vector is given by:
[tex] |v| = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
[tex]|v| = \sqrt{ {6}^{2} + {( - 2)}^{2} } [/tex]
[tex]|v| = \sqrt{ 36+ 4 } [/tex]
[tex]|v| = \sqrt{40} = 2 \sqrt{10} [/tex]
