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If two pairs of opposite edges of a tetrahedron art; at right angles, then the third pair
- a)is also at right angles always
- b)can never be at right angle
- c)is inclined at. some acute angle
- d)is inclined at some obtuse an
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If two pairs of opposite edges of a tetrahedron art; at right angles, ...
Let the coordinates of the vertices O, A, B, C o f tetrahedron be (α, β, γ), (a, 0, 0), (0, b, 0) and (0. 0, c) respectively. Then it is given that
OA is perpendicular to BC
and OB is perpendicular to CA
To prove that
OC is perpendicular to AB
OA is perpendicular to BC
and OB is perpendicular to CA
To prove that
OC is perpendicular to AB
Most Upvoted Answer
If two pairs of opposite edges of a tetrahedron art; at right angles, ...
Explanation:
Given: Two pairs of opposite edges of a tetrahedron are at right angles.
Statement: The third pair of opposite edges is also at right angles always.
This explanation illustrates that when two pairs of opposite edges of a tetrahedron are at right angles, the third pair must also be at right angles in order to maintain the structure and meet at a common vertex.
Given: Two pairs of opposite edges of a tetrahedron are at right angles.
Statement: The third pair of opposite edges is also at right angles always.
- Proof: Let's consider a tetrahedron with two pairs of opposite edges at right angles. This means that the edges are perpendicular to each other.
- Now, let's visualize the tetrahedron: Since the two pairs of opposite edges are at right angles, they form a perpendicular intersection. This creates a structure similar to a triangular pyramid with the perpendicular edges as the base and height.
- Considering the third pair of opposite edges: In a tetrahedron, the third pair of opposite edges must meet at a common vertex with the other edges. Since the two pairs of opposite edges are at right angles, the third pair must also be at right angles in order to meet at a common vertex.
- Conclusion: Therefore, if two pairs of opposite edges of a tetrahedron are at right angles, the third pair of opposite edges will also be at right angles always.
This explanation illustrates that when two pairs of opposite edges of a tetrahedron are at right angles, the third pair must also be at right angles in order to maintain the structure and meet at a common vertex.
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Community Answer
If two pairs of opposite edges of a tetrahedron art; at right angles, ...
Let the coordinates of the vertices O, A, B, C o f tetrahedron be (α, β, γ), (a, 0, 0), (0, b, 0) and (0. 0, c) respectively. Then it is given that
OA is perpendicular to BC
and OB is perpendicular to CA
To prove that
OC is perpendicular to AB
OA is perpendicular to BC
and OB is perpendicular to CA
To prove that
OC is perpendicular to AB
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If two pairs of opposite edges of a tetrahedron art; at right angles, then the third paira)is also at right angles alwaysb)can never be at right anglec)is inclined at. some acute angled)is inclined at some obtuse anCorrect answer is option 'A'. Can you explain this answer?
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