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A ladder leans against the ground, the plane z = 0. The… | StemPy Lab
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A ladder leans against the ground, the plane z = 0. The direction of the ladder has ratios (2, 3, 6). Which expression gives the angle φ between the ladder and the ground?
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High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
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A ladder leans against the ground, the plane
z
=
0
z = 0
z
=
0
. The direction of the ladder has ratios
(
2
,
3
,
6
)
(2, 3, 6)
(
2
,
3
,
6
)
. Which expression gives the angle
φ
\varphi
φ
between the ladder and the ground?
cos
−
1
6
7
\cos^{-1}\dfrac{6}{7}
cos
−
1
7
6
sin
−
1
3
7
\sin^{-1}\dfrac{3}{7}
sin
−
1
7
3
sin
−
1
2
7
\sin^{-1}\dfrac{2}{7}
sin
−
1
7
2
sin
−
1
6
7
\sin^{-1}\dfrac{6}{7}
sin
−
1
7
6
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A lamp is at the point (1, -2, 3) and a ceiling lies in the plane 6x - 3y + 2z = 4, with lengths in metres. What is the shortest distance from the lamp to the ceiling? →
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