The resultant of two vectors P and Q is Ř If Q is
doubled then the new resultant vector is perpendicular
to P. Then magnitude of Ř is:
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2
Answer:
Let the angle between two vectors
P
and
Q
be
α
and their resultant is
R
So we can write
R
2
=
P
2
+
Q
2
+
2
P
Q
cos
α
...
...
[
1
]
When Q is doubled then let the resultant vector be
R
1
, So we can write
R
2
1
=
P
2
+
4
Q
2
+
4
P
Q
cos
α
...
...
[
2
]
Again by the given condition
R
1
is perpendicular to
P
So
4
Q
2
=
P
2
+
R
2
1
...
...
[
3
]
Combining [2] and [3] we get
R
2
1
=
P
2
+
P
2
+
R
2
1
+
4
P
Q
cos
α
⇒
2
P
Q
cos
α
=
−
P
2
...
...
[
4
]
combining [1] and [4] we get
R
2
=
P
2
+
Q
2
−
P
2
⇒
R
=
Q
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