A tetrahedron has vertices P 1 , 2 , 1 , Q 2 , 1 , 3 , R - 1 , 1 , 2 and O 0 , 0 , 0 . The angle between the faces O P Q and P Q R is

Question

A tetrahedron has vertices P 1 , 2 , 1 , Q 2 , 1 , 3 , R - 1 , 1 , 2 and O 0 , 0 , 0 . The angle between the faces O P Q and P Q R is, cos - 1 ⁡ 7 31, c o s - 1 17 31, c o s - 1 19 35, c o s - 1 9 35

MARKS App · Accepted Answer

Vector perpendicular to face O P Q = i ^ j ^ k ^ 1 2 1 2 1 3 = 5 i ^ - j ^ - 3 k ^ Vector perpendicular to face P Q R = i ^ j ^ k ^ 2 1 - 1 1 - 1 2 = i ^ - 5 j ^ - 3 k ^ Angle between two faces c o s θ = 5 + 5 + 9 35 35 = 19 35 ⇒ θ = c o s - 1 19 35

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