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Byju's Answer
Standard XII
Mathematics
Property 4
The vector ...
Question
The vector
^
i
+
^
j
can be expressed as complex number by
A
e
i
π
4
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B
√
2
e
i
π
4
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C
e
i
π
2
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D
none of these
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Solution
The correct option is
B
√
2
e
i
π
4
In complex no.
1
+
i
⟹
√
2
[
cos
(
π
/
4
)
+
sin
(
π
/
4
)
]
=
√
2
e
i
π
/
4
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Similar questions
Q.
If
arg
(
z
)
denotes the principal argument of a complex number
z
, then the value of the expression
arg
(
−
i
e
i
π
9
.
z
2
)
+
2
arg
(
2
i
e
−
i
π
18
.
¯
z
)
is
Q.
A vector of magnitude
√
2
coplanar with the vectors
→
a
=
^
i
+
^
j
+
2
^
k
and
→
b
=
^
i
+
2
^
j
+
^
k
and perpendicular to the vector
→
c
=
^
i
+
^
j
+
^
k
is
(1)
−
^
i
−
^
k
(2)
^
j
−
^
k
(3)
^
i
−
^
j
(4)
^
i
+
^
k
Q.
Which of the following is a unit vector in the direction of
^
i
+
^
j
+
^
k
.
Q.
A unit vector in the direction of resultant vector of
→
A
= -2
^
i
+3
^
j
+
^
k
and
→
B
=
^
i
+2
^
j
-4
^
k
is
Q.
Let,
→
a
=
^
i
+
2
^
j
+
^
k
,
→
b
=
^
i
−
^
j
+
^
k
,
→
c
=
^
i
+
^
j
−
^
k
.
A vector coplanar to
→
a
and
→
b
has a projection along
→
c
of magnitude
1
√
3
, then the vector is
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