If A 
, B 
and C 
are three non collinear points and origin does not lie in the plane of the points A, B and C, then for any point P 
in the plane of the Δ ABC, prove that ;
(i) 
(ii) A point 
is on plane of Δ ABC such that vector 
is ⊥ to plane of Δ ABC. Then show that
= 
, where 
is the vector area of the Δ ABC.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) P lies in the plane of A, B and C
. 
⇒ 
⇒ 
= 0 ⇒ 
. 
= 
Hence (i) is proved
(ii) Let 
= λ 
Since 
. 
= 
Proved is part (i)
∴λ 
= 
⇒ 
∴ 
= 
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