Question

Given that P = (7, 16) and Q = (-1, 7), find the component form and magnitude of vector QP .

Answer 1

QP = (8, 9) and | QP | = √145

QP = p - q = (7, 16 ) - ( - 1,7) = ( 7 + 1, 16 - 7) = (8, 9)

given a vector (x , y) then magnitude = √x² + y²

|QP | = | 8² + 9² = √145

Answer 2

Magnitude is

`√(145)`

Explanation:

Given that position vector of P is

(7,16) and Q is (-1,7)

Hence vector QP = coordinates of P-coordinates of Q

= (8,9)

We can write QP = 8i+9j

where 8 is the component along horizontal x axis and 9 the component along vertical y axis.

Magnitude of QP = [tex]\sqrt{8^9^2} \\=\sqrt{145} \\