Question

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

• A. ${30}^0$
• B. ${60}^0$
• C. ${90}^0$
• D. ${120}^0$

Answer 1

Answer: (C)

${90}^0$

Let the position vectors of the vertices be$\overline{o},\overline{a},\overline{b}and\overline{c}.$
One opposite pair= $\overline{a}.(\overline{b}-\overline{c})=0$
hence,$a.b=a.c$
Similarly from other pair $b.a=b.c$
Hence , from these 2 equations, $a.b=b.c=a.c$

Hence $c.(a-b)=a.c-b.c=0$
Hence proved