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Mathematics
Mathematics
Problem
A straight line '
L
L
L
' cuts the lines
A
B
,
A
C
AB, AC
A
B
,
A
C
and
A
D
AD
A
D
of a parallelogram
A
B
C
D
ABCD
A
B
C
D
at points
B
1
,
C
1
B_1, C_1
B
1
,
C
1
and
D
1
D_1
D
1
, respectively. If
A
B
1
=
λ
1
A
B
,
A
D
1
=
λ
2
A
D
AB_1 = \lambda_1 AB, AD_1 = \lambda_2 AD
A
B
1
=
λ
1
A
B
,
A
D
1
=
λ
2
A
D
and
A
C
1
=
λ
3
A
C
AC_1 = \lambda_3 AC
A
C
1
=
λ
3
A
C
, then
1
λ
3
\frac{1}{\lambda_3}
λ
3
1
is equal to a.
1
λ
1
+
1
λ
2
\frac{1}{\lambda_1} + \frac{1}{\lambda_2}
λ
1
1
+
λ
2
1
b.
1
λ
1
−
1
λ
2
\frac{1}{\lambda_1} - \frac{1}{\lambda_2}
λ
1
1
−
λ
2
1
c.
−
λ
1
+
λ
2
-\lambda_1 + \lambda_2
−
λ
1
+
λ
2
d.
λ
1
+
λ
2
\lambda_1 + \lambda_2
λ
1
+
λ
2
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