find a vector which is parallel to v = i -2jand has a magnitude 10
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Explanation:
The given parallel vector is
→
a
=
i
−
2
j
.
The magnitude of the vector is
|
b
|
=
10
.
The expression for the unit vector is,
ˆ
a
=
→
a
√
x
2
+
y
2
Here, x is the coefficient of the variable in the x-direction and y is the coefficient of the variable in the y-direction.
Substitute the given values in the above expression.
ˆ
a
=
i
−
2
j
√
1
2
+
2
2
=
1
√
5
(
i
−
2
j
)
The expression for the vector that is parallel to the vector
→
a
=
i
−
2
j
is,
→
b
=
|
b
|
ˆ
a
Substitute the given values in the above expression.
→
b
=
10
×
1
√
5
(
i
−
2
j
)
=
2
√
5
(
i
−
2
j
)
=
2
√
5
i
−
4
√
5
j
Thus, the require vector is
2
√
5
i
−
4
√
5
j
.
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