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Byju's Answer
Standard XII
Mathematics
Orthogonal System of Vectors
The number of...
Question
The number of vectors of unit length perpendicular to vectors
a
→
=
i
^
+
j
^
and
b
→
=
j
^
+
k
^
is
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
_
.
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Solution
The unit vector perpendicular to
a
→
and
b
→
is
given by
±
a
→
×
b
→
a
→
×
b
→
for
a
→
=
i
^
+
j
^
and
b
→
=
j
^
+
k
^
a
→
×
b
→
=
i
^
j
^
k
^
1
1
0
0
1
1
=
i
^
1
-
0
-
j
^
1
-
0
+
k
^
1
-
0
a
→
×
b
→
=
i
^
-
j
^
+
k
^
i
.
e
.
a
→
×
b
→
=
1
+
1
+
1
=
3
∴
number
of
unit
vectors
perpendicular
to
a
→
and
b
→
is
two
i
.
e
±
i
^
-
j
^
+
k
^
3
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