What angle does this vector (1,6,-5) make with the XY plane?

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thilina-g | College Teacher | (Level 1) Educator

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The equation of xy plane is `n = (0,0,1).`

The line is `b = (1,6,-5)`

The angle between the line and xy plane is A

`n.b = |n||b| sinA`

`(0,0,1).(1,6,-5) = |(0,0,1)|xx |(1,6,-5)| xx sinA`

`-5 = 1 xx sqrt(62) xx sinA`

`sinA = (-5)/sqrt(62)`

`sinA = -0.6350`

`A = -39.42` degrees.

 

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