Question

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

Answer 1

The magnitude of the vector is
$\sqrt{2 {}^{2} + 5 {}^{2} } = \sqrt{29}$
the component form is
<2,5>

Answer 2

To find the component form, <x2-x1, y2-y1>
We have P(2,9) meaning, x1=2, y1=9
And, Q(4,14) meaning, x2=4, y2=14
Now PQ = <4-2, 14-9> = <2, 5>

Now to find the magnitude, we use the distance formula aka the Pythagorean Theorem. a^2 + b^2 = c^2 and we have, x=2, y=5
So, 2^2 + 5^2 = c^2 =29
Therefore, the magnitude is c = sqrt of 29.