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Byju's Answer
Standard XII
Physics
Unit Vectors
Find a vector...
Question
Find a vector of magnitude 5 units, and parallel to the resultant of the vectors.
→
a
=
2
^
i
+
3
^
j
−
^
k
and
→
b
=
^
i
−
2
^
j
+
^
k
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Solution
Given two vectors are
→
a
=
2
^
i
+
3
^
j
−
^
k
and
→
b
=
^
i
−
2
^
j
+
^
k
If
→
c
is the resultant vector of
→
a
and
→
b
=
(
2
^
i
+
3
^
j
−
^
k
)
+
(
^
i
−
2
^
j
+
^
k
)
=
3
^
i
+
^
j
+
0.
^
k
Now, a vector having magnitude
5
and parallel to
→
c
is given by
5
→
c
|
→
c
|
=
5
(
3
^
i
+
^
j
0
^
k
)
√
3
2
+
1
2
+
0
2
=
15
√
10
^
i
+
5
√
10
^
j
It is required vector.
[ Note : A vector having magnitude
I
and parallel to
→
a
is given by
I
→
a
|
→
a
|
.
]
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Similar questions
Q.
Find unit vector perpendicular to the plane of the vectors,
→
A
=
^
i
−
2
^
j
+
^
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and
→
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−
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.
Q.
If
→
a
=
^
i
+
^
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+
^
k
,
→
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2
^
i
−
^
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^
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and
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c
=
^
i
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^
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find a unit vector parallel to the vector.
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−
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+
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→
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Q.
Find the vector parallel to the vector
^
i
−
2
^
j
and has magnitude
2
√
5
units.
Q.
Find unit vectors perpendicular to the plane of the vectors,
→
A
=
^
i
−
2
^
j
+
^
k
and
→
B
=
2
^
i
−
^
k
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→
A
=
^
i
−
2
^
j
+
^
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→
B
=
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^
i
+
3
^
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−
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