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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
If A⃗ = 2î ...
Question
If
→
A
=
2
^
i
+
^
j
+
^
k
and
→
B
=
^
i
+
^
j
+
^
k
are two vectors, then the unit vector is
A
Perpendicular to
→
A
is
−
^
j
+
^
k
√
2
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B
Parallel to
→
A
is
2
^
i
+
^
j
+
^
k
√
6
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C
Perpendicular to
→
B
is
(
^
j
+
^
k
√
2
)
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D
Parallel to
→
A
is
^
i
+
^
j
+
^
k
√
3
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Solution
The correct options are
A
Perpendicular to
→
A
is
−
^
j
+
^
k
√
2
C
Perpendicular to
→
B
is
(
^
j
+
^
k
√
2
)
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0
Similar questions
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
Q.
If
→
a
=
2
^
i
+
4
^
j
−
5
^
k
,
→
b
=
^
i
+
^
j
+
^
k
,
→
c
=
^
j
+
2
^
k
, then the unit vectors parallel to
→
a
+
→
b
+
→
c
is
Q.
Component of
→
a
=
^
i
−
^
j
−
^
k
perpendicular to the vector
→
b
=
2
^
i
+
^
j
−
^
k
is?
Q.
Vectors
→
a
=
3
^
i
+
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
2
^
k
a
n
d
→
c
=
2
^
i
−
^
j
−
^
k
. Find vector
→
d
if
¯
d
is perpendicular to
→
c
and
→
d
.
→
a
=
10
,
→
b
=
1
Q.
A
: Vector perpendicular to both
^
i
+
^
j
+
^
k
and
2
^
i
+
^
j
+
3
^
k
is
2
^
i
−
^
j
−
^
k
R
: Every vector perpendicular to plane containing
→
a
,
→
b
is equal to
→
a
×
→
b
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