Q.

The vertices of a triangle are (2,3,5), (−1,3,2) , (3,5,−2), then the angles are

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a

300,300,1200

b

Cos−115,900,Cos−153

c

300,600,900

d

Cos−113,900,Cos−123

answer is D.

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Detailed Solution

Let A(2,3,5),B(−1,3,2),C(3,5,−2)D.r’s of AB↔ are (−1−2,3−3,2−5) =(−3,0,−3)=(1,0,1), D.r’s of  BC↔ are  (3+1,5−3,−2−2)=(4,2,−4)=(2,1,−2)D.r’s of CA↔ are (3−2,5−3,−2−5)=(1,2,−7)If α is an angle between AB↔,AC↔ then Cosα=13⇒α=Cos−113If  β is an angle between BC↔,AB↔ then Cosβ=0⇒β=900 If γ is an angle between BC↔,CA↔ then γ=Cos−123Angles of the triangle are Cos−113,900,Cos−123
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