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Byju's Answer
Standard XII
Mathematics
Properties of Determinants
If x, y, z ...
Question
If
x
,
y
,
z
∈
R
&
Δ
=
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
2
x
5
x
+
2
y
7
x
+
5
y
+
2
z
3
x
7
x
+
3
y
9
x
+
7
y
+
3
z
∣
∣ ∣
∣
=
−
16
then value of
x
is
A
−
2
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B
−
3
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C
2
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D
3
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Solution
The correct option is
C
−
2
Given,
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
2
x
5
x
+
2
y
7
x
+
5
y
+
2
z
3
x
7
x
+
3
y
9
x
+
7
y
+
3
z
∣
∣ ∣
∣
=
−
16
[
R
′
2
=
R
2
−
2
×
R
1
and
R
′
3
=
R
3
−
3
×
R
1
]
or,
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
0
3
x
5
x
+
3
y
0
4
x
6
x
+
4
y
∣
∣ ∣
∣
=
−
16
or,
x
{
18
x
2
+
12
x
y
−
20
x
2
−
12
x
y
}
=
−
16
or,
−
2
x
3
=
−
16
or,
x
3
=
8
or,
x
=
2
.
Suggest Corrections
0
Similar questions
Q.
If
x
,
y
,
z
∈
R
&
△
=
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
2
x
5
x
+
2
y
7
x
+
5
y
+
2
z
3
x
7
x
+
3
y
9
x
+
7
y
+
3
z
∣
∣ ∣
∣
=
−
16
then value of
x
is
Q.
If
x
,
y
,
z
∈
R
,
Δ
=
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
2
x
5
x
+
2
y
7
x
+
5
y
+
2
z
3
x
7
x
+
3
y
9
x
+
7
y
+
3
z
∣
∣ ∣
∣
=
−
16
, then the real value of
x
is
Q.
The line
x
−
2
4
=
y
+
1
−
1
=
z
−
1
3
is perpendicular to the plane
(
a
)
2
x
−
y
+
z
=
3
(
b
)
4
x
−
y
+
3
z
=
1
(
c
)
4
x
+
y
+
3
z
=
1
(
d
)
x
+
7
y
+
z
=
3
Q.
The line
x
−
2
4
=
y
+
1
−
1
=
z
−
1
3
is perpendicular to the plane
Q.
If
∣
∣ ∣
∣
x
x
+
y
x
+
y
+
z
2
x
3
x
+
2
y
4
x
+
3
y
+
2
z
3
x
6
x
=
3
y
10
x
+
6
y
+
3
z
∣
∣ ∣
∣
=
64
, then the real value of
x
is .........
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