Question

Given that P = (5, 8) and Q = (6, 9), find the component form and magnitude of vector PQ.

Answer 1

((x2-x1),(y2-y1))
((6-5),(9-8))
Component form: (1,1)
(1^2+1^2)^(1/2)
Magnitude: (2)^(1/2)

Answer 2

Explanation:

Given : P = (5, 8) and Q = (6, 9)

To find: the component form and magnitude of vector PQ.

Solution: It is given that P = (5, 8) and Q = (6, 9).

The component form of the vector PQ is given as:

`Vector PQ=Q-P`

`Vector PQ=<6-5,9-8>`

`Vector PQ=<1,1>`

The magnitude of vector PQ is given as:

`|<x,y>|=√(x^2+y^2)`

`|<x,y>|=√((1)^2+(1)^2)`

`|<x,y>|=√(2)`

`|<x,y>|=1.414`

Thus, the component form of the vector PQ is
`Vector PQ=<1,1>` and the magnitude form is
`|<x,y>|=1.414`.