Question

Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ

Answer 1

Component form:

`\binom{ - 16}{2}`

2. Magnitude

`2√(65)`

Step-by-step explanation

Given that P = (-5, 5) and Q = (-13, 6),

Vector PQ

`= \binom{ - 13}{6} - \binom{ - 5}{5}`

`= \binom{ - 13 + 5}{6 - 5}`

`= \binom{ - 8}{1}`

2 vector PQ

`= 2 \binom{ - 8}{1}`

`= \binom{ - 16}{2}`

This is the component form.

The magnitude is given by

`= \sqrt{ {x}^(2) + {y}^(2) }`

`= \sqrt{ {( - 16)}^(2) + {2}^(2) }`

`= √(256 + 4)`

`= √(260)`

`= 2√(65)`