four students in traditional dresses represent 4 states of India standing at the points represented by O(0,0,0), A(a,0,0),B(0,b,0),C(0,0,c) find - Maths - Introduction to Three Dimensional Geometry

Question

four students in traditional dresses represent 4 states of India
standing at the points represented by O(0,0,0),
A(a,0,0),B(0,b,0),C(0,0,c) find the place in terms of coordinates
where girl representing "Bharat Mata" be replaced so that "Bharat
Mata" is equidistant from the four students

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

We O0,0,0, Aa,0,0 B0,b,0 and C0,0,cLet coordinates of required point be Dp,q,rAccording to questiom:OD=AD=BD=CD= d units SayOD=p-02+q-02+r-02=d⇒p2+q2+r2=d⇒p2+q2+r2=d2 ;iAD=p-a2+q-02+r-02=d⇒p-a2+q2+r2=d⇒p-a2+q2+r2=d2 ;iiBD=p-02+q-b2+r-02=d⇒p2+q-b2+r2=d⇒p2+q-b2+r2=d2 ;iiiCD=p-02+q-02+r-c2=d⇒p2+q2+r-c2=d⇒p2+q2+r-c2=d2 ;ivBy i and ii, we get:p-a2+q2+r2=p2+q2+r2⇒p-a2=p2⇒p2+a2-2ap=p2⇒a2-2ap=0⇒2ap=a2⇒p=a2Similarly by i and iii, you will get q=b2 and by i and iv, you will get:r=c2Hence p,q,r=a2,b2,c2Hence coordinates of required points are a2,b2,c2
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four students in traditional dresses represent 4 states of India standing at the points represented by O(0,0,0), A(a,0,0),B(0,b,0),C(0,0,c). find the place in terms of coordinates where girl representing "Bharat Mata" be replaced so that "Bharat Mata" is equidistant from the four students.