# 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 √(a^{2} + b^{2})

= √(-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.