What is the relationship between the perpendiculars in a 3D vector?

  • Thread starter lionely
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In summary, We are discussing a problem involving finding the components of a vector in a triangle. The k component is determined to be 5, but there is confusion about the i and j components. By dropping perpendiculars DP and EQ onto the base of the triangle, we can determine that the i component is 4 and the j component is 4j. It is also mentioned that the perpendiculars are located at the midpoints of the base diagonals, and the distance between them, PQ, can be compared to the length of the base.
  • #1
lionely
576
2

Homework Statement



pbul0.png


I'm confused ,here's ... my attempt..

all I know so far is the

the k component would be 5...
I have no idea what to do with the i and j
 
Last edited:
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  • #2
hi lionely! :smile:
lionely said:
all I know so far is the

the k component would be 5...
I have no idea what to do with the i and j

drop perpendiculars DP and EQ onto the base …

where are P and Q in relation to ABCD ? :wink:​
 
  • #3
Hint: Assume DE is located such that its midpoint is positioned directly over the intersection of the base diagonals OB and AC.
 
  • #4
Hmm is DE is assumed to be at the mid point then.. for the j component that would be 4j

but the i? ... umm is it like the base below DE is 8 because DE is 6cm and OA is 14? so 14-6?
 
  • #5
tiny-tim said:
hi lionely! :smile:


drop perpendiculars DP and EQ onto the base …

where are P and Q in relation to ABCD ? :wink:​

when I dropped the perpendiculars they ended up being at the midpoints of the widths of the base
 
  • #6
lionely said:
Hmm is DE is assumed to be at the mid point then.. for the j component that would be 4j

but the i? ... umm is it like the base below DE is 8 because DE is 6cm and OA is 14? so 14-6?

You had your answer in this post, but didn't realize it. 14 - 6 = 8, and this difference is split evenly between between the two sides. So the i component is 4.
 
  • #7
hi lionely! :smile:

(just got up :zzz:)
lionely said:
when I dropped the perpendiculars they ended up being at the midpoints of the widths of the base

(we'll call them P and Q)

ok … so the next line in your proof would be to say what the distance PQ is

and then you can compare that with the length of the base :wink:
 

What is a 3d vector?

A 3d vector is a mathematical representation of a point in 3-dimensional space, consisting of three components: x, y, and z. It is commonly used in computer graphics and physics to describe the position, direction, and magnitude of an object.

How do you find the magnitude of a 3d vector?

The magnitude of a 3d vector can be found using the Pythagorean theorem. The magnitude is equal to the square root of the sum of the squares of the three components (x, y, and z).

What is the difference between a 3d vector and a 2d vector?

A 3d vector has three components (x, y, and z) while a 2d vector has only two components (x and y). This means that a 3d vector can represent a point in 3-dimensional space, while a 2d vector can only represent a point in 2-dimensional space.

How do you add two 3d vectors?

To add two 3d vectors, you simply add the corresponding components (x, y, and z) of each vector. For example, to add vector A = (2, 3, 4) and vector B = (5, 6, 7), the resulting vector would be C = (2+5, 3+6, 4+7) = (7, 9, 11).

What are some real-world applications of 3d vectors?

3d vectors have many practical applications, including computer graphics, video game development, 3d modeling, physics simulations, and navigation systems. They are also used in engineering, architecture, and robotics to calculate distances, angles, and forces in 3-dimensional space.

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