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vector homework problem that I have no idea about?
A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (0, 0, 0), (1, 2, 0), and (0, 1, 3). By what angle does the tower now deviate from the vertical?
2 Answers
- Al PLv 71 decade agoFavorite Answer
Let:
A = 1i ,2j ,0k
B = 0i ,1j ,3k
Tower's current direction vector
C = A X B = 6i -3j 1k
Let:
A = 6i ,-3j ,1k
B = 0i ,0j ,1k
A dot B = 1
|A| = 6.782330
|B| = 1.000000
cos(a) = (A dot B) / |A| |B| = 0.147442
Answer:
Arccos = ( 0.147442 )= 1.422815 rad
OR:
Arccos ( 0.147442 )= 81.5213 degrees
- Rob MLv 41 decade ago
the three coordinates give you two vectors.
(1-0)i+(2-0)j+(0-0)k and (0-0)i+(1-0)k+(3-0)k
if you take the cross product of these two vectors you get the new perpendicular of the surface. This cross product yields
6i-3j+k
If you take the dot product of this versus the vector k (which was the original vector of the tower before it drifted and solve for the angle it now makes we get
(6i-3j+k) . (k) /(â6^2+3^2+1^2 =cos(θ) solve for θ
