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Mathematics
Mathematics
Problem
Find the value of
λ
\lambda
λ
so that the points
P
,
Q
,
R
P, Q, R
P
,
Q
,
R
and
S
S
S
on the sides
O
A
,
O
B
,
O
C
OA, OB, OC
O
A
,
O
B
,
O
C
and
A
B
AB
A
B
, respectively, of a regular tetrahedron
O
A
B
C
OABC
O
A
B
C
are coplanar. It is given that
O
P
O
A
=
1
3
,
O
Q
O
B
=
1
2
,
O
R
O
C
=
1
3
\frac{OP}{OA} = \frac{1}{3}, \frac{OQ}{OB} = \frac{1}{2}, \frac{OR}{OC} = \frac{1}{3}
O
A
O
P
=
3
1
,
O
B
O
Q
=
2
1
,
O
C
O
R
=
3
1
and
O
S
A
B
=
λ
\frac{OS}{AB} = \lambda
A
B
O
S
=
λ
. a.
λ
=
1
2
\lambda = \frac{1}{2}
λ
=
2
1
b.
λ
=
−
1
\lambda = -1
λ
=
−
1
c.
λ
=
0
\lambda = 0
λ
=
0
d. for no value of
λ
\lambda
λ
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