Question

Given that P=(7,5) and Q= (8,8), find the component form and magnitude of the vector PQ

Answer 1

Component form:

$\overrightarrow{PQ} = i(Q_x - P_x) + j(Q_y - P_y) = i(8-7) + j(8-5) = i + 3j = (1,3)$

Magnitude:

$\lVert\overrightarrow{PQ}\rVert = \sqrt{PQ_x^2 + PQ_y^2} = \sqrt{1^2 + 3^2} = \sqrt{10} \approx 3.16$