A(x,y,z)P(0,3,2),Q(2,0,3),R(0,0.1) ⇓ As A is in xy-plane ⇒A(x,y,0) AP2=AQ2 (x−0)2+(y−3)2+(0−2)2=(x−2)2+(y−0)2 +(0−3)2 x2+y2−6y+9+4=x2−4x+4+y2+9 ⇒−6y=−4x ⇒2x=3y AP2=AR2 x2+y2−6y+9+4=x2+y2+1 ⇒y=2 ⇒x=3 A(3,2,0),B(1,4,−1),C(2,0,−2)
→
AB
=−2
∧
i
+2
∧
j
−
∧
k
→
BC
=
∧
i
−4
∧
j
−
∧
k
→
AC
=−
∧
i
−2
∧
j
−2
∧
k
→
AB
⋅
→
AC
=2−4+2=0 ⇒△ABC is right angle triangle at A Also, AB=3,BC=3√2,AC=3 ⇒AB=AC ar(△ABC)=
