Finding Reflection of a Vector

Thread starter gipc
Start date Nov 23, 2011
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Reflection Vector

In summary, the reflection of a vector is the mirror image of a vector across a given line or plane. It is calculated by projecting the vector onto the line/plane and finding the perpendicular vector, and it can be negative. This concept is significant in various fields and has real-life applications in designing mirrors, predicting light behavior, and creating 3D graphics.

Nov 23, 2011

gipc

Find the reflection v' of v=i-3j+2k around the line i-k

how can I do that? I am extremely rusty with math these days;

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Nov 23, 2011

LCKurtz

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Call i-k = W. I would calculate the vector projection of V on W, call it V_p. Then the reflected vector is 2V_p-V. Draw a little triangle/parallelogram and you will see it.

1. What is the concept of finding reflection of a vector?

The reflection of a vector is the process of finding the mirror image of a vector across a given line or plane. This is often used in mathematics and physics to solve problems involving symmetry and geometric transformations.

2. How is the reflection of a vector calculated?

The reflection of a vector is calculated by projecting the vector onto the line or plane of reflection and then finding the perpendicular vector to the line or plane. This perpendicular vector is then subtracted from the original vector to obtain the reflection vector.

3. Can the reflection of a vector be negative?

Yes, the reflection of a vector can be negative. This occurs when the vector is reflected across a line or plane that is not the x, y, or z-axis. In this case, the direction of the vector will change, resulting in a negative value.

4. What is the significance of finding reflection of a vector?

Finding the reflection of a vector is important in various fields such as physics, computer graphics, and engineering. It allows us to understand and predict how objects will behave when reflected, and it helps us solve complex problems involving symmetry and transformations.

5. Are there any real-life applications of finding reflection of a vector?

Yes, there are many real-life applications of finding reflection of a vector. For example, it is used in designing mirrors and reflective surfaces, in predicting the behavior of light rays, and in creating 3D graphics and animations. It is also used in fields such as architecture, robotics, and game development.