In the figure express vector c and vector d in terms of vector a and vector b . Find a vector in direction of vector a=vector i - 2 vector j that has magnitude 7 units.
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Answer:
a
=
i
^
−2
j
^
=1
i
^
−2
j
^
+0
k
^
Magnitude of
a
=
1
2
+(−2)
2
+0
2
∣
a
∣=
1+4+0
=
5
Unit vector in direction of
a
^
=
magnitudeof
a
1
×
a
a
^
=
5
1
[1
i
^
+2
j
^
+0
k
^
]
a
^
=
5
1
i
^
−
5
2
j
^
+0
k
^
a
^
=
5
1
i
^
−
5
2
j
^
Thus, Vector having a magnitude
1=
5
1
i
^
−
5
2
j
^
Vector having a magnitude
7=7[
5
1
i
^
−
5
2
j
^
]
=
5
7
i
^
−
5
14
j
^
=
5
7
(
i
^
−2
j
^
) (By taking common
5
7
)
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