The equations of the hypotenuse of a right angled isosceles triangle are 5 x + 6 = 3 y + 10 = 8 z + 14 and the centroid of the triangle is ( 3 20 , − 1 , 3 16 ) . If ( α , β , γ ) is the cir

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The equations of the hypotenuse of a right angled isosceles triangle are 5 x + 6 ​ = 3 y + 10 ​ = 8 z + 14 ​ and the centroid of the triangle is ( 3 20 ​ , − 1 , 3 16 ​ ) . If ( α , β , γ ) is the circumcentre of the triangle then γ =

TestHub · Accepted Answer

Let a = 5 i + 3 j + 8 k be parallel to the given line, G = ( 3 20 ​ , − 1 , 3 16 ​ ) and P = ( 5 λ − 6 , 3 λ − 10 , 8 λ − 14 ) a point on the hypotenuse. The circumcentre is the mid-point of the hypotenuse, which is the foot of the perpendicular from G , so GP ⋅ a ˙ = 0 . This gives 98 λ = 245 , λ = 2 5 ​ , and γ = 8 ⋅ 2 5 ​ − 14 = 6 .

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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