Que: the resultant of two vectors P bar and Q bar is R bar. If the magnitude of Q bar is doubled ,the new resultant becomes perpendicular to P bar , then magnitude of R bar
Answers
Answer:
If Q is doubled then the new resultant vector is perpendicular to P. Then R is equal to : 9.P
+
Q
=
R
Resultant of
P
&
Q
is given as
∣
∣
∣
∣
R
∣
∣
∣
∣
2
=
∣
∣
∣
∣
P
∣
∣
∣
∣
2
+
∣
∣
∣
∣
Q
∣
∣
∣
∣
2
+2
∣
∣
∣
∣
P
∣
∣
∣
∣
∣
∣
∣
∣
Q
∣
∣
∣
∣
cosθ⟶(i)
When Q is doubled, new resultant R
1
is perpendicular to
P
0
⇒(R
1
).
P
=0
(
P
+2
Q
).
P
=0
∣
∣
∣
∣
P
∣
∣
∣
∣
2
+2
∣
∣
∣
∣
P
∣
∣
∣
∣
.
∣
∣
∣
∣
Q
∣
∣
∣
∣
cosθ=0
cosθ=
2
∣
∣
∣
∣
Q
∣
∣
∣
∣
−
∣
∣
∣
∣
P
∣
∣
∣
∣
putting value of cosθ in eqn (i)
∣
∣
∣
∣
R
∣
∣
∣
∣
2
=
∣
∣
∣
∣
P
∣
∣
∣
∣
2
+
∣
∣
∣
∣
Q
∣
∣
∣
∣
2
+2
∣
∣
∣
∣
P
∣
∣
∣
∣
∣
∣
∣
∣
Q
∣
∣
∣
∣
⎣
⎢
⎡
2
∣
∣
∣
∣
Q
∣
∣
∣
∣
−
∣
∣
∣
∣
P
∣
∣
∣
∣
⎦
⎥
⎤
∣
∣
∣
∣
R
∣
∣
∣
∣
2
=
∣
∣
∣
∣
P
∣
∣
∣
∣
2
−
∣
∣
∣
∣
P
∣
∣
∣
∣
2
+
∣
∣
∣
∣
Q
∣
∣
∣
∣
2
∣
∣
∣
∣
R
∣
∣
∣
∣
2
=
∣
∣
∣
∣
Q
∣
∣
∣
∣
2
∣
∣
∣
∣
R
∣
∣
∣
∣
=
∣
∣
∣
∣
Q
∣
∣
∣
∣
∣
∣
∣
∣
R
∣
∣
∣
∣
=
∣
∣
∣
∣
Q
∣
∣
∣
∣