two vectors of magnitudes 4 and 6 are acting through a point. if the magnitude of the resultant is r
Answers
Explanation:
Let 'a' be a vector whose magnitude is 6 units.
and 'b' be a vector whose magnitude is 4 units.
and their resultant is R at any angle (say alpha)
Now,
its resultant
(0 < \alpha < 180)(0<α<180)
should lie in between the angle 0 degrees to 180 degrees.
Case-1.
\sf \alpha = 0^{\circ}α=0
∘
vector formula
\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha ) }R=
a
2
+b
2
+2abcos(α)
\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab}R=
a
2
+b
2
+2ab
as cos 0 is 1.
\sf R = a + bR=a+b
\sf R = 6 + 4R=6+4
\sf R = 10 \: unitsR=10units
Case-2
\sf \alpha = 180^{\circ}α=180
∘
\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha )}R=
a
2
+b
2
+2abcos(α)
\sf R = \sqrt{ {a}^{2} + {b}^{2} - 2ab}R=
a
2
+b
2
−2ab
as cos 180 is -1.
\sf R = a - bR=a−b
\sf R = 6 - 4R=6−4
\sf R = 2 \: unitsR=2units
so, the resultant R will be in between these values.
Therefore, the resultant R will be in between these values.