Mathematics: Find the magnitude of vector v that has an initial point of (1,3) and a terminal point of (7,1)

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Find the magnitude of vector v that has an initial

starajaclark1429

05.01.2022

ANSWER

$|v| = 2 \sqrt{10}$

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.

$v = \binom{7}{1} - \binom{1}{3}$

$v = \binom{7 - 1}{1 - 3}$

$v = \binom{6}{ - 2}$

The magnitude of the vector is given by:

$|v| = \sqrt{ {x}^{2} + {y}^{2} }$

$|v| = \sqrt{ {6}^{2} + {( - 2)}^{2} }$

$|v| = \sqrt{ 36+ 4 }$

$|v| = \sqrt{40} = 2 \sqrt{10}$

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