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The figure shows a cube of edge 1 unit with a corner O… | StemPy Lab
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The figure shows a cube of edge 1 unit with a corner O at the origin. The red line is the body diagonal OG and the blue edge OA lies along the x-axis. What is the angle between OG and OA?
Mathematics
Hard
High School (11–12)
Vectors and Three-Dimensional Geometry › Three-Dimensional Geometry
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The figure shows a cube of edge
1
1
1
unit with a corner
O
O
O
at the origin. The red line is the body diagonal
O
G
OG
O
G
and the blue edge
O
A
OA
O
A
lies along the
x
x
x
-axis. What is the angle between
O
G
OG
O
G
and
O
A
OA
O
A
?
Fig. 1: A cube of edge 1 with one corner O at the origin and three edges along the x, y and z axes. The opposite corner is labelled G. A red line joins O to G, the body diagonal, and the edge OA along the x-axis is drawn in blue. The other edges are thin grey lines.
cos
−
1
1
2
\cos^{-1}\dfrac{1}{2}
cos
−
1
2
1
cos
−
1
1
2
\cos^{-1}\dfrac{1}{\sqrt{2}}
cos
−
1
2
1
cos
−
1
2
3
\cos^{-1}\sqrt{\dfrac{2}{3}}
cos
−
1
3
2
cos
−
1
1
3
\cos^{-1}\dfrac{1}{\sqrt{3}}
cos
−
1
3
1
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