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Byju's Answer
Standard XII
Mathematics
Equation of a Line Passing through 2 Points
The system of...
Question
The system of equations
−
2
x
+
y
+
z
=
a
,
x
−
2
y
+
z
=
b
,
x
+
y
−
2
z
=
c
has:
A
no solution if
a
+
b
+
c
≠
0
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B
unique solution if
a
+
b
+
c
=
0
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C
infinte number of solutions if
a
+
b
+
c
=
0
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D
infinte solution if
a
+
b
+
c
≠
0
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Solution
The correct option is
C
infinte number of solutions if
a
+
b
+
c
=
0
Δ
=
∣
∣ ∣
∣
−
2
1
1
1
−
2
1
1
1
−
2
∣
∣ ∣
∣
=
0
Δ
x
=
∣
∣ ∣
∣
a
1
1
b
−
2
1
c
1
−
2
∣
∣ ∣
∣
=
3
a
+
3
b
+
3
c
Δ
y
=
∣
∣ ∣
∣
−
2
a
1
1
−
b
1
1
c
−
2
∣
∣ ∣
∣
=
3
a
+
3
b
+
3
c
Δ
z
=
∣
∣ ∣
∣
−
2
1
a
1
−
2
b
1
1
c
∣
∣ ∣
∣
=
3
a
+
3
b
+
3
c
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0
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Q.
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Equation of a Line Passing through 2 Points
Standard XII Mathematics
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