Vectors and Lines - Confirmation

In summary, the conversation is about finding the vector BD in a parallelogram with known points A, C, and the midpoint of AB. The person used the midpoint formula to find point B, then found AB and D, and finally BD. They are unsure if their method was correct and are seeking confirmation.
  • #1
vg19
67
0
Hey,

I just would like confirmation on this question.
A parallelogram has sides A,B, BC, CD, DA. Given A(1,-1,2), C(2,1,0) and the midpoint M(1,0,-3) of AB, find BD(vector).

This is what I did. To find point B, I used the midpoint formula

(1,0,-3) = 1/2[(x+1), (-1+y), (2+z)]

Solving that, I got B as (1,1,-8)

I then found AB = (1,1,-8) - (1,-1,2) = (0,2,-10)

I then found D by saying (2,1,0) - (0,2,-10) = (2,-1,10)

Finally BD = (2,-1,10) - (1,1,-8) = (1,-2,18)

Im not sure if I did this correctly of even if my method at all was correct. Any confirmation would be much apprecieated.
 
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  • #2
looks good to me
 

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

A vector is a mathematical object that has both magnitude (size) and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction. On the other hand, a line is a geometric object that extends infinitely in both directions. It is represented by a straight line with no endpoints.

2. How do you perform vector addition?

Vector addition is performed by adding the corresponding components of two vectors. For example, if vector A is represented as [Ax, Ay] and vector B is represented as [Bx, By], then the sum of the two vectors (A + B) is [Ax + Bx, Ay + By]. This can also be visualized using the parallelogram rule or the head-to-tail method.

3. What does it mean for two vectors to be orthogonal?

Two vectors are orthogonal if they are perpendicular to each other, meaning that their dot product is equal to 0. This means that the angle between the two vectors is 90 degrees. Orthogonality is important in many applications, such as in finding the shortest distance between a point and a line.

4. How do you calculate the magnitude of a vector?

The magnitude (or length) of a vector can be calculated using the Pythagorean theorem. If a vector is represented as [x, y], then its magnitude can be calculated as √(x2 + y2). Another way to calculate the magnitude of a vector is by taking the square root of the dot product of the vector with itself, which is √(x2 + y2).

5. What are some real-life applications of vectors and lines?

Vectors and lines have many applications in various fields, such as physics, engineering, and computer graphics. Some examples include calculating forces and velocities in physics, designing structures in engineering, and creating 3D graphics in computer games. They are also used in navigation, such as in determining the direction and distance between two points on a map.

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