Let P be the plane 
x + 2y + 3z = 16 and let
Let 
and 
be three distinct vectors in S such that 
. Let V be the volume of the parallelepiped determined by vectors 
and 
. Then the value of 
V is
Text Solution
Verified by Experts45
(45)
Given 
is an equilateral 
Now distances of U, V, W from P = 
Also, Distance of plane P from origin
OQ = 4
OP = OQ - PQ 
OP = 
Hence, 
Also, for 
UVW, P is circumcenter
for 
UVW : US = Rcos30°
UV = 2Rcos30°
Volume of tetrahedron with coterminous edges 
parallelopiped with coterminous edges
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