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JEE Main 6 Apr 2024 Shift 1 Solved Paper
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© examsnet.com
Question : 21
Total: 89
Let
α
β
γ
=
45
;
α
,
β
,
γ
∈
R
. If
x
(
α
,
1
,
2
)
+
y
(
1
,
β
,
2
)
+
z
(
2
,
3
,
γ
)
=
(
0
,
0
,
0
)
for some
x
,
y
,
z
∈
R
,
x
y
z
≠
0 , then
6
α
+
4
β
+
γ
is equal to _______.
[6 Apr 2024 Shift 1]
Your Answer:
Validate
Solution:
👈: Video Solution
α
β
γ
=
45
,
α
β
γ
∈
R
x
(
α
,
1
,
2
)
+
y
(
1
,
β
,
2
)
+
z
(
2
,
3
,
γ
)
=
(
0
,
0
,
0
)
x
,
y
,
z
∈
R
,
x
y
z
≠
0
α
x
+
y
+
2
z
=
0
x
+
β
y
+
3
z
=
0
2
x
+
2
y
+
γ
z
=
0
x
y
z
≠
0
⇒
non-trivial
|
α
1
2
1
β
3
2
2
γ
|
=
0
⇒
α
(
β
γ
−
6
)
−
1
(
γ
−
6
)
+
2
(
2
−
2
β
)
=
0
⇒
α
β
γ
−
6
α
−
γ
+
6
+
4
−
4
β
=
0
⇒
6
α
+
4
β
+
γ
=
55
© examsnet.com
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