# Help needed with direction angles and vector equations

• agenttiny200
In summary, the question involves finding the vector equation of a line with direction angles of 60°, 45°, and 60° passing through the point (1, -2, 5). The hint given by the teacher involves using trig ratios and the unit vector formula, but the person asking the question has been struggling for a week and is seeking help as a last resort.
agenttiny200

## Homework Statement

A line has direction angles 60°, 45°, 60° and passes through the point
(1, -2, 5). Determine the vector equation of this line.

## Homework Equations

I honestly have no clue. My teacher gave a hint it has to do with trig (as in the trig ratios) and the unit vector formula, but I don't see how they mix.

## The Attempt at a Solution

Tried everything except the right way for the last week, resulting in dead ends.

if no one has a clue, it would help to mention that, proving to my teacher that he should just give me the answer.

And I am serious when I say I have been trying for a week to solve it, I am not trying to get by easily. posting my questions here is kind of a last resort, for a question that I am really stuck on.

## 1. What are direction angles and vector equations?

Direction angles are the angles formed between a vector and a set of coordinate axes, usually the x, y, and z axes. Vector equations are mathematical expressions that represent the relationship between vectors in a space.

## 2. How do I calculate direction angles?

To calculate direction angles, you can use trigonometric functions such as sine, cosine, and tangent. First, find the magnitude of the vector using the Pythagorean theorem. Then, use the trigonometric functions to find the direction angles by dividing each component of the vector by the magnitude.

## 3. What is the difference between direction angles and vector components?

Direction angles and vector components are related but represent different aspects of a vector. Direction angles describe the orientation of a vector in a space, while vector components represent the magnitude and direction of the vector in each coordinate axis.

## 4. How do I write a vector equation?

To write a vector equation, you need to first identify the direction and magnitude of the vector. Then, you can express the vector in terms of its components or using the unit vector notation. The equation should also include the operations and any constants involved in the vector calculation.

## 5. What are some real-life applications of direction angles and vector equations?

Direction angles and vector equations have practical applications in various fields such as physics, engineering, and navigation. They are used to analyze and describe the motion and forces of objects, design structures and machines, and determine the location and direction of movement in navigation systems.

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