MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Formation of Algebraic Expressions

Prove that if...

Question

Prove that if two pairs of opposite edges at a tetrahedrun are orthogonal then third part is also orthogonal.

Open in App

Solution

Let ABCD our tetrahedron such that AB $⊥$ DC and AC $⊥$ BD
We need to prove that AD $⊥$ BC
Indeed, let $\to D A = \to a, \to D B = \to b$ and $\to D C = \to c$
Thus, $\to c \cdot (\to a - \to b) = 0$ and
$\to b \cdot (\to a - \to c) = 0$ which gives
$\to a \cdot \to c = \to b \cdot \to c$ and $\to a \cdot \to b = \to b \cdot \to c$
which gives $\to a \cdot \to c = \to a \cdot \to b$
or $\to a \cdot (\to b - \to c) = 0$ or AD $⊥$ BC.

Suggest Corrections

thumbs-up

0

Similar questions

Q. Prove that if in tetrahedron , two pair of opposite edges are orthogonal, so is the third pair.

Q. If in a tetrahedron, edges in each of the two pairs of opposite edges are perpendicular, then show that the edges in the third pair are also perpendicular.

Q. In a tetrahedron if two pairs of opposite edges are at a right angles then the third pair is inclined at an angle of

Q. If two pairs of opposite edges of a tetrahedron are perpendicular, then

Q. If two circles cut a third circle orthogonally then prove that their radical axis or their common chord will pass through the centre of the third circle.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Formation of Algebraic Expressions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Formation of Algebraic Expressions

Standard VI Mathematics

Join BYJU'S Learning Program

CrossIcon