The resultant vector Ę and © is Ř. On reversing the direction of 7, Qthe resultant vector becomes S.
Then R
a) p2-Q?
b) p2 +Q?
c) 2(P2 +Q2) d) 2P2 +Q?
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Answer:
Let θ be angle between
A
and
B
.∴ Resultant of
A
and
B
is
P=
A
2
+B
2
+2ABcosθ
---(i)
When
B
is reversed, then the angle between
A
and -
B
is (180
∘
- θ).Resultant of
A
and -
B
is
Q =
A
2
+B
2
+2ABcos(180
∘
−θ)
Q =
A
2
+B
2
+2ABcosθ
--(ii)
Squaring and adding (i) and (ii), we getP
2
+Q
2
=2(A
2
+B
2
)
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