Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

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 -

`|| v || = v_(1)^2 + v_(2)^2`

Which could be rewritten as the following, in terms of the initial and terminal points -

`|| v || =√(( P2 - P1^2 ) + ( Q1 - Q2)^2)`

Let's substitute known values and calculate || v || -

`|| v || =√(( P2 - P1^2 ) + ( Q1 - Q2)^2),\\- 2 - 3, 6 - ( - 1 )\\< - 5, 7 >\\-------------------------\\|| v || = √( ( - 5 )^2 + ( 7 )^2),\\|| v || = √( 25 + 49),\\|| v || = √(74)`

Solution = Option B!

Answer 2

The answer is √74 = 8.6023

Magnitude of a line between two points can be written as

√( c - a)² + ( d - b)²

Where (a,b) and (c ,d) are two points

A(3,-1) and B(-2,6)

Magnitude of AB = √ ( -2 - 3)² + ( 6 + 1)²

= √ (-5)² + 7²

= √ 25 + 49

= √74 units = 8.6023 units

Hope this helps you.