Solveeit Logo
Login

Question

Question: Let OABC be a tetrahedron whose edges are of unit length. If \(\overline { \mathrm { OA } }\) = <im...

Let OABC be a tetrahedron whose edges are of unit length. If

OA‾\overline { \mathrm { OA } } = , OB‾\overline { \mathrm { OB } } = b‾\overline { \mathrm { b } }

and OC‾\overline { \mathrm { OC } } = α(aˉ+bˉ)+β(aˉ×bˉ)\alpha ( \bar { a } + \bar { b } ) + \beta ( \bar { a } \times \bar { b } ) , then βα\frac { \beta } { \alpha } is equal to-

A

1/21 / \sqrt { 2 }

B

2\sqrt { 2 }

C

2

D

222 \sqrt { 2 }

Answer

222 \sqrt { 2 }

Explanation

Solution

= α(aˉ+bˉ)+β(aˉ×bˉ)\alpha ( \bar { a } + \bar { b } ) + \beta ( \bar { a } \times \bar { b } ) ̃ 12c‾⋅a‾\frac { 1 } { 2 } \overline { \mathrm { c } } \cdot \overline { \mathrm { a } } = 3α2\frac { 3 \alpha } { 2 }

̃ a = 13\frac { 1 } { 3 } , = β(32)2\beta \left( \frac { \sqrt { 3 } } { 2 } \right) ^ { 2 }

̃ b = 223\frac { 2 \sqrt { 2 } } { 3 }

̃ βα\frac { \beta } { \alpha } = 222 \sqrt { 2 }