Suppose a cable car moves with direction vector vec(d) = ((2),(-2),(1)) The question asks, "at what angle to the horizontal does the cable car travel?". By horizontal, if you assume the x-axis, the angle can be found using (|vec(a) * vec(b)|)/(|vec(a) vec(b)|). Using this, the angle I find between vec(d) and ((2),(0),(0)) The angle I find is 48.2^(circ)

moiraudjpdn 2022-08-12 Answered
Suppose a cable car moves with direction vector d
( 2 2 1 )
The question asks, "at what angle to the horizontal does the cable car travel?". By horizontal, if you assume the x-axis, the angle can be found using
| a b | | a b |
) Using this, the angle I find between d and
( 2 0 0 )
The angle I find is 48.2 . If I use the z-vector instead:
( 0 0 1 )
The angle I find is 70.5
The answer is 19.5 . How would I get this value?
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Answers (2)

trazonombresrg
Answered 2022-08-13 Author has 8 answers
You have to find the angle between d and the projection of d onto the horizontal plane, which is the vector p = ( 2 , 2 , 0 ). Try to apply the same equation with those two vectors.
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Landon Wolf
Answered 2022-08-14 Author has 4 answers
Horizontal' here means the x,y plane.
If you sketch a picture, it could be clear that the angle of a vector and a plane and the angle with a normal vector of the plane adds up to 90
So, since you already found the angle with the z -axis to be 70.5 , the angle to the horizontal will be 90 70.5 = 19.5
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