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Byju's Answer
Standard XII
Mathematics
Orthogonal System of Vectors
If a → is a u...
Question
If
a
→
is a unit vector such that
a
→
×
i
^
=
j
^
,
find
a
→
.
i
^
.
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Solution
We know
k
^
×
i
^
=
j
^
.
.
.
(
1
)
Given
:
a
→
×
i
^
=
j
^
.
.
.
(
2
)
Comparing (1) and (2), we get
a
→
=
k
^
Now,
a
→
.
i
^
=
k
^
.
i
^
=
0
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Similar questions
Q.
If
→
a
is a unit vector such that
→
a
×
^
i
=
^
j
, find
→
a
.
^
i
Q.
Let
→
a
=
→
i
−
→
j
,
→
b
=
→
j
−
→
k
,
→
c
=
→
k
−
→
i
. If
→
d
is a unit vector such that
→
a
⋅
→
d
=
[
→
b
→
c
→
d
]
=
0
,
then
→
d
is equal to
Q.
A non-zero vector
→
a
is such that its projections along vectors
ˆ
i
+
ˆ
j
√
2
,
−
ˆ
i
+
ˆ
j
√
2
and
ˆ
k
are equal, then unit vector along
→
a
is
Q.
If
a
=
i
−
j
,
b
=
i
+
j
,
c
=
i
+
3
j
+
5
k
and
n
is a unit vector such that
b
,
n
=
0
,
a
,
n
=
0
then the value of
|
c
,
n
|
is equal to
Q.
Let
→
u
=
ˆ
i
+
ˆ
j
,
→
v
=
ˆ
i
−
ˆ
j
a
n
d
→
w
=
ˆ
i
+
2
ˆ
j
+
3
ˆ
k
. If
ˆ
n
is a unit vector such that
→
u
.
ˆ
n
=
0
a
n
d
→
v
.
ˆ
n
=
0
then
∣
∣
→
w
.
ˆ
n
∣
∣
is equal to
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Standard XII Mathematics
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