What figure do these 3D vectors make?

In summary, the given points A, B, and C form a collinear line. This is determined by finding the vectors AB, BC, and CA and calculating their magnitudes using the pythagorean theorem. Since all three magnitudes are equal, the points are collinear and do not form a specific type of figure.
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Homework Statement


The vertices of a figure are given by A(-8, 4, -2), B(-6, 3, 5), and C(-10, 5, -9). What type of figure is ABC? Why?

Homework Equations


pythagorean theorem: |AB|=√(x^2+y^2+z^2)

The Attempt at a Solution


I first found the vector AB, BC, and CA by subtracting the components of the vectors.
Then I calculation the magnitude of |AB|, |BC|, and |CA| using the pythagorean theorem.
I got this |AB|=3√6 |BC|=6√6 and |CA|=3√6
According to my calculation, point A is on the line connecting points B and C, so the 3 points are collinear and form a line.

But the answer seems wrong since they are asking for a type of a figure.
 
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  • #2
The vectors are indeed linearly interdependent, your conclusion is correct.
 

Related to What figure do these 3D vectors make?

1. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. In other words, a scalar is a single number, while a vector is a combination of numbers that indicate both the size and direction of the quantity.

2. How can you determine the direction of a 3D vector?

To determine the direction of a 3D vector, you can use the trigonometric functions sine, cosine, and tangent. These functions can be used to calculate the angles between the vector and each of the three axes (x, y, and z).

3. What is the cross product of two 3D vectors?

The cross product of two 3D vectors is a vector that is perpendicular to both of the original vectors. It is calculated by taking the product of the magnitudes of the two vectors, multiplied by the sine of the angle between them, and then multiplied by a unit vector perpendicular to both of the original vectors.

4. How do you find the magnitude of a 3D vector?

The magnitude of a 3D vector can be found using the Pythagorean theorem. This involves taking the square root of the sum of the squares of the vector's components (x, y, and z). Alternatively, you can also use the dot product of the vector with itself and then take the square root of the result.

5. Can 3D vectors be added or subtracted?

Yes, 3D vectors can be added and subtracted using the same rules as 2D vectors. This involves adding or subtracting the corresponding components (x, y, and z) of the two vectors. The result is a new vector with the same dimensionality as the original vectors.

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