We are being asked to determine the magnitude of a vector here, given the initial and terminal points. This would be in the form < v1, v2 >, so that you could state the following -
[tex]|| v || = v_{1}^2 + v_{2}^2[/tex]
Which could be rewritten as the following, in terms of the initial and terminal points -
[tex]|| v || =\sqrt{( P2 - P1^2 ) + ( Q1 - Q2)^2}[/tex]
Let's substitute known values and calculate || v || -
[tex]|| v || =\sqrt{( P2 - P1^2 ) + ( Q1 - Q2)^2},\\- 2 - 3, 6 - ( - 1 )\\< - 5, 7 >\\-------------------------\\|| v || = \sqrt{ ( - 5 )^2 + ( 7 )^2},\\|| v || = \sqrt{ 25 + 49},\\|| v || = \sqrt{74}[/tex]
Solution = Option B!
