Let the position vectors of the points A, B, C and D be 
and 
. Let the set S = { 
R: the points A, B, C and D are coplanar}. The 
equal to
Text Solution
Verified by ExpertsD
Given that:
A(5,5,2 
),B(l,2,3),C(-2, 
,4)and
D(-1,5,6).
Now,
Given that A, B, C and D are coplanar.
Expand the determinant along the first row.
-4[( 
- 5)(6 - 2 
)-0]-(-3)[-7(6 - 2 
)-(-6)(4 - 2 
)]+(3 - 2 
)[0 -(-6)( 
- 5)]
On solving the above equation we get,
= 3, 
= 2
We have two values of 
.
= (3 + 2) 2 + (2 + 2) 2 =41
Hence, 
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