Question

Find the horizontal and vertical components of the vector with the given length and direction, and write the vector in terms of the vectors i and j.|v|=38, θ=120 degrees

Answer 1

`v=-19\vec{i}+32.91\vec{j}`

Step-by-step explanation:

Given that:

• Length of the vector, |v|=38

,

• Direction, θ=120 degrees

To find the horizontal and vertical components of the vector, we use the rule:

`v=|v|\cos \theta\vec{i}+|v|\sin \theta\vec{j}`

Substituting the given values, we have:

`\begin{gathered} v=38\cos 120\vec{i}+38\sin 120\vec{j} \\ =-19\vec{i}+19\sqrt[]{3}\vec{j} \\ v=-19\vec{i}+32.91\vec{j} \end{gathered}`