Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of the vector PQ.

Solution:

Given: P = (2, 9) and Q = (4, 14)

We know that PQ vector can be expressed as P' - Q'

PQ = P' - Q' = (2i + 9j) - (4i + 14j)

= (2 - 4)i + (9 - 14)j =

-2i - 5j

Component form of -2i - 5j is (-2, -5)

Magnitude form can be expressed as √(a² + b²)

= √(-2)² + (-5)² 

= √(4 + 25)

= √29

Therefore, the component form and magnitude of the vector PQ are (-2, -5) and √29.

Given that P = (2, 9) and Q = (4, 14), find the component form and magnitude of the vector PQ.

Summary:

If P = (2, 9) and Q = (4, 14), then the component form and magnitude of the vector PQ are (-2, -5) and √29 respectively.