The angle made by the vector vec A=2hat i+3hat j with x -axis and y -axis respectively are
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2
Answer:
Given
OA
=
i
^
+
j
^
+
k
^
;
OB
=
i
^
−
j
^
+2
k
^
and
OC
=2
j
^
−
k
^
AB
=−2
j
^
+
k
^
and
AC
=−
i
^
+
j
^
−2
k
^
AB
×
AC
=3
i
^
−
j
^
−2
k
^
let the required unit vector be
r
=x
i
^
+y
j
^
+z
k
^
As
r
is parallel to the plane determined by ABC.
r
is perpendicular to
AB
×
AC
⇒3x−y−2z=0 -----(1)
given
r
is also perpendicular to
i
^
+
k
^
⇒x+z=0 -----(2)
r
is an unit vector.
⇒x
2
+y
2
+z
2
=1 ----(3)
solving equations (1),(2) and (3) gives
x=±
3
3
1
;y=±
3
3
5
and z=∓
3
3
1
∴
r
=±
3
3
1
(
i
^
+5
j
^
−
k
^
)
Hence, option A.
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