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Byju's Answer
Standard XII
Mathematics
Family of Planes Passing through the Intersection of Two Planes
Directions : ...
Question
Directions :
> stands for =
< stands for ≠
× stands for >
+ stands for <
= stands for
≯
- stands for
≮
If α − β × γ, it does not imply that:
A
α
−
β
<
γ
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B
α
×
β
>
γ
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C
α
+
β
×
γ
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D
α
−
β
>
γ
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Solution
The correct options are
A
α
−
β
<
γ
C
α
+
β
×
γ
α
−
β
×
γ
=
α
≮
β
>
γ
If we are taking only one direction, then either of the B and D are possible.
So A and C are not possible.
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Similar questions
Q.
For
α
,
β
,
γ
,
θ
ϵ
R
. Let
A
θ
(
α
,
β
,
γ
)
=
∣
∣ ∣ ∣
∣
cos
(
α
+
θ
)
sin
(
α
+
θ
)
1
cos
(
β
+
θ
)
sin
(
β
+
θ
)
1
cos
(
γ
+
θ
)
sin
(
γ
+
θ
)
1
∣
∣ ∣ ∣
∣
If
α
,
β
,
γ
are fixed. then
y
=
A
x
(
α
,
β
,
γ
)
represents
Q.
Prove that
∣
∣ ∣ ∣
∣
(
β
+
γ
−
α
−
δ
)
4
(
β
+
γ
−
α
−
δ
)
2
1
(
γ
+
α
−
β
−
δ
)
4
(
γ
+
α
−
β
−
δ
)
2
1
(
α
+
β
−
γ
−
δ
)
4
(
α
+
β
−
γ
−
δ
)
2
1
∣
∣ ∣ ∣
∣
=
−
64
(
α
−
β
)
(
α
−
γ
)
(
α
−
δ
)
(
β
−
γ
)
(
β
−
δ
)
(
γ
−
δ
)
Q.
cos
(
α
+
β
+
γ
)
+
cos
(
α
−
β
−
γ
)
+
cos
(
β
−
γ
−
α
)
+
cos
(
γ
−
α
−
β
)
=
Q.
If
α
,
β
,
γ
are the roots of
a
x
3
+
b
x
2
+
c
x
+
d
=
0
and
∣
∣ ∣ ∣
∣
α
β
γ
β
γ
α
γ
α
β
∣
∣ ∣ ∣
∣
=
0
,
α
≠
β
≠
γ
, then find the equation whose roots are
α
+
β
−
γ
,
γ
+
α
−
β
,
β
+
γ
−
α
Q.
α
,
β
,
γ
are roots of
x
3
−
2
x
2
−
x
+
2
=
0
. Centroid of triangle with vertices
(
α
,
β
,
γ
)
,
(
β
,
γ
,
α
)
,
(
γ
,
α
,
β
)
is
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