A vector = i cap + 2j cap - 4k cap , B vector = 2i cap - 3j cap - 6k cap . Find A vector . B vector
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Answer:
Step 1: Calculation of component of
a
along
i
^
+
j
^
Let
b
=
i
^
+
j
^
The unit vector
b
^
b
^
=
∣
i
^
+
j
^
∣
i
^
+
j
^
=
2
1
(
i
^
+
j
^
)
Component of vector
a
along
b
vector
=acosθ
=a
∣ab∣
a
.
b
=
b
a
.
b
=
a
.
b
^
To get the vector form, (
a
.
b
^
)
b
^
=[(2
i
^
+3
j
^
).
2
1
(
i
^
+
j
^
)]
2
1
(
i
^
+
j
^
) =[
2
1
(2+3)]
2
1
(
i
^
+
j
^
)
=
2
5
(
i
^
+
j
^
)
Step 2: Component of
a
along
i
^
−
j
^
Let
c
=
i
^
−
j
^
Unit vector,
c
^
=
2
1
(
i
^
−
j
^
)
Component of vector
a
along
c
vector
=(
a
.
c
^
)
c
^
=[(2
i
^
+3
j
^
).
2
1
(
i
^
−
j
^
)]
2
1
(
i
^
−
j
^
) =[−
2
1
]
2
1
(
i
^
−
j
^
)
=
2
−1
i
^
+
2
1
j
^
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