- #1
vertciel
- 63
- 0
Hello everyone,
Thank you in advance for your help!
---
10. A vector [itex] \vec{u} [/itex] with direction angles A1, B1, and Y1, is perpendicular to a vector [itex] \vec{v} [/itex] with direction angles A2, B2, and Y2. Prove that:
[itex] \cos A1 \cos B2 + \cos B1 \cos B2 + \cos Y1 \cos Y2 = 0[/itex].
---
I let [itex] \vec{u} = [a, b, c], \vec{v} = [x, y, z] [/itex].
Since these are perpendicular, therefore:
[itex] \vec{u} \bullet \vec{v} = ax + by + cz = 0 [/itex].
Also, [itex] a, b, c, x, y, z [/itex] would all correspond to their direction cosines.
However, I do not understand how I can prove the above statement with these facts. For example, would [itex] \cos A1 \cos A2 = 0 [/itex] simply because they are the components of two vectors which are parallel to each other?
Thank you in advance for your help!
---
Homework Statement
10. A vector [itex] \vec{u} [/itex] with direction angles A1, B1, and Y1, is perpendicular to a vector [itex] \vec{v} [/itex] with direction angles A2, B2, and Y2. Prove that:
[itex] \cos A1 \cos B2 + \cos B1 \cos B2 + \cos Y1 \cos Y2 = 0[/itex].
---
The Attempt at a Solution
I let [itex] \vec{u} = [a, b, c], \vec{v} = [x, y, z] [/itex].
Since these are perpendicular, therefore:
[itex] \vec{u} \bullet \vec{v} = ax + by + cz = 0 [/itex].
Also, [itex] a, b, c, x, y, z [/itex] would all correspond to their direction cosines.
However, I do not understand how I can prove the above statement with these facts. For example, would [itex] \cos A1 \cos A2 = 0 [/itex] simply because they are the components of two vectors which are parallel to each other?