The component ofa→=2iˆ+3jˆa→=2i^+3j^ along the direction of vectors (iˆ+jˆ)(i^+j^) and (iˆ−jˆ)(i^−j^) respectively are______
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Answer:
Let the given vector be
a
=2
i
^
+3
j
^
To find the component of 'a' along
i
^
+
j
^
we have to find unit vector along
i
^
+
j
^
Let the unit vector be
a
^
a
^
=
∣
i
^
+
j
^
i
^
+
j
^
=
2
1
(
i
^
+
j
^
)
Component of
a
along
i
^
+
j
^
=(
a
⋅
a
^
)
a
^
=[(2
i
^
+3
j
^
)⋅
2
1
(
i
^
+
j
^
)]
2
1
(
i
^
+
j
^
)
=[
2
1
(2+3)]
2
1
(
i
^
+
j
^
)
=
2
5
[
2
1
(
i
^
+
j
^
)]
=
2
5
i
^
+
2
5
j
^
Component of
a
along
i
^
−
j
^
=(
a
⋅
a
^
)
a
^
=[(2
i
^
+3
j
^
)⋅
2
1
(
i
^
−
j
^
)]
2
1
(
i
^
−
j
^
)
=[
2
1
(2−3)]
2
1
(
i
^
−
j
^
)
=
2
−1
[
2
1
(
i
^
−
j
^
)]
=−
2
1
i
^
+
2
1
j
^
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