Given a = 2i+3j and b= i+j.what is the component of vector a perpendicular to vector b and in the same pane as b
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Answer:
We know, (
i
+
j
)(
i
−
j
)=0
Vector (
i
−
j
) is perpendicular to
B
.
Let, (
i
−
j
) =
C
Now, (
A
.
C
)=(2
i
+3
j
)(
i
−
j
)
The required component is:
(
A
.
C
)
C
C
=2
i
+3
j
)(
i
−
j
)
∣
∣
∣
∣
i
−
j
∣
∣
∣
∣
(
i
−
j
)
(
A
.
C
)
C
C
=−
2
1
(
i
−
j
).......(since, C=
(1+1)
=
2
)
(
A
.
C
)
C
C
=
2
1
(
j
−
i
)
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