Question

TRIGONOMETRY Find the magnitude and the direction of the resultant vector

Answer 1

Step 1:

Write the given vectors

`\begin{gathered} \bar{V}\text{ = ( 10 , 9 )} \\ \bar{W}\text{ = (-6 , -2 )} \end{gathered}`

Step 2

Resultant vector = [ 10 + (-6) , 9 + (-2) ]

= ( 4 , 7 )

Resultant vector = 4i + 7j

Step 3

`\begin{gathered} \text{Magnitude = }\sqrt[]{4^2+7^2} \\ \text{Magnitude = }\sqrt[]{16\text{ + 49}} \\ \text{Magnitude = }\sqrt[]{65} \\ \text{Magnitude = 8.1} \end{gathered}`

Step 4:

`\begin{gathered} \text{Direction }\theta=tan^(-1)((4)/(7)) \\ \text{Direction = 29.7} \end{gathered}`