Given that p = (5, 9) and q = (13, 12), find the component form and magnitude of vector pq.

ANSWER

The vector in the component form is


and the magnitude is



EXPLANATION

The given points are P=(5,9) and Q=(13,12).

We want to find the component form of vector PQ.

Let the components of vector PQ be



Vector PQ can express in terms of position vectors as follows:

This implies that;



We subtract the corresponding components to get;


The vector in component form is



The magnitude of vector PQ is