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Byju's Answer
Standard XII
Mathematics
Cross Product of Two Vectors
Let a⃗ =î -...
Question
Let
→
a
=
^
i
−
^
k
,
→
b
=
x
^
i
+
^
j
+
(
1
−
x
)
^
k
and
→
c
=
y
^
i
+
x
^
j
+
(
1
+
x
−
y
)
^
k
, then
[
→
a
,
→
b
,
→
c
]
depends on
A
Only
4
y
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B
Only
x
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C
Both
x
and
y
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D
Neither
x
nor
y
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Solution
The correct option is
C
Neither
x
nor
y
Given
→
a
=
^
i
−
^
k
→
b
=
x
^
i
+
^
j
+
(
1
−
x
)
^
k
→
c
=
y
^
i
+
x
^
j
+
(
1
+
x
−
y
)
^
k
We have
[
→
a
→
b
→
c
]
=
→
a
.
(
→
b
×
→
c
)
Now,
→
b
×
→
c
=
∣
∣ ∣ ∣
∣
^
i
^
j
^
k
x
1
1
−
x
y
x
1
+
x
−
y
∣
∣ ∣ ∣
∣
=
^
i
(
1
+
x
−
x
−
x
2
)
−
^
j
(
x
+
x
2
−
x
y
−
y
+
x
y
)
+
^
k
(
x
2
−
y
)
⇒
→
a
(
→
b
×
→
c
)
=
1
Which does not depend on
x
and
y
Suggest Corrections
0
Similar questions
Q.
Let
→
a
=
^
i
−
^
k
,
→
b
=
x
^
i
+
^
j
+
(
1
−
x
)
^
k
and
→
c
=
y
^
i
+
x
^
j
+
(
1
+
x
−
y
)
^
k
,
then
[
→
a
→
b
→
c
]
depends on
Q.
If
¯
a
=
^
i
−
^
k
,
¯
b
=
x
^
i
+
^
j
+
(
1
−
x
)
^
k
and
¯
c
=
y
^
i
+
x
^
j
+
(
1
+
x
−
y
)
^
k
, then
[
¯
a
¯
b
¯
c
]
depends on
Q.
Let
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
−
3
^
i
+
^
k
and
→
c
=
^
i
+
2
^
j
+
3
^
k
, then the ascending order of magnitudes of
A
)
[
→
a
×
→
b
→
b
×
→
c
→
c
×
→
a
]
B
)
[
→
a
+
→
b
→
b
+
→
c
→
c
+
→
a
]
C
)
[
→
a
→
b
→
c
]
[
→
a
→
b
→
c
]
−
1
D
)
[
→
a
−
→
b
→
b
−
→
c
→
c
−
→
a
]
Q.
If the vectors
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
,
→
c
=
x
^
i
+
(
x
−
2
)
^
j
−
^
k
are coplanar, then
x
=
Q.
If
→
a
=
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
and
→
a
=
^
i
−
^
j
−
^
k
, then
(
→
a
×
→
b
)
×
(
→
c
×
→
d
)
is a vector orthogonal to both
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