Question

In Problems 65-72, find the direction angle of $\mathbf{v}$. $\mathbf{v}=-3 \sqrt{3} \mathbf{i}+3 \mathbf{j}$

   In Problems 65-72, find the direction angle of $\mathbf{v}$.
 $\mathbf{v}=-3 \sqrt{3} \mathbf{i}+3 \mathbf{j}$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan 4th Edition

Chapter 8, Problem 67

Instant Answer

Step 1

The vector given is \(\mathbf{v} = -3 \sqrt{3} \mathbf{i} + 3 \mathbf{j}\). This means the vector \(\mathbf{v}\) has a horizontal component of \(-3 \sqrt{3}\) and a vertical component of \(3\). Show more…

Show all steps

lock

Thanks for your feedback!

In Problems 65-72, find the direction angle of $\mathbf{v}$. $\mathbf{v}=-3 \sqrt{3} \mathbf{i}+3 \mathbf{j}$

Play audio

Feedback

Powered by NumerAI

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, particularly the arctan function, are used to determine the angle corresponding to a given tangent value. When finding the direction angle of a vector, the correct quadrant must be considered to ensure the computed angle accurately reflects the vector's orientation.

Direction Angle

The direction angle of a vector is the angle it makes with the positive x-axis. It is used to describe the orientation of the vector in the plane, and is calculated using the inverse tangent function of the ratio of the y-component to the x-component, with adjustments made based on the quadrant where the vector lies.

Vector

A vector is a quantity that has both magnitude and direction. It is typically represented by its components along the coordinate axes, which are essential in determining its characteristics such as direction and length.

Component Form

Expressing a vector in component form (using i and j for the horizontal and vertical directions respectively) allows for an easy determination of the individual parts of the vector. This breakdown is crucial when calculating properties like magnitude and the angle of the vector relative to a coordinate axis.

Recommended Videos

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later