Question

Find the magnitude of a vector v, whose initial point is (7, -2) and terminal point is (4,3). Approximateyour answer to the nearest hundredth

Answer 1

Concept

The magnitude of a vector PQ is the distance between the initial point P and the end point Q . In symbols the magnitude of PQ is written as | PQ | . If the coordinates of the initial point and the end point of a vector is given, the Distance Formula can be used to find its magnitude.

Given data

Initial point = ( 7, -2 )

Terminal point = ( 4, 3 )

Apply the distance formula below to find the magnitude of the vector V.

`V\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}\text{ }`

x1 = 7 y1 = -2

x2 = 4 y2 = 3

Substitute the values in the formula to find the magnitude.

`\begin{gathered} V\text{ = }\sqrt[]{(3-(-2))^2+(4-7)^2} \\ =\text{ }\sqrt[]{(3+2)^2+(-3)^2} \\ =\text{ }\sqrt[]{5^2\text{ + 9}} \\ =\text{ }\sqrt[]{25\text{ + 9}} \\ =\text{ }\sqrt[]{34} \end{gathered}`

Magnitude of vector V = 5.83