Question

Q)Two vectors of magnitudes 4 and 6 are acting
through a point. If the magnitude of the
resultant is R
a) 4<R<6
b) 4<R< 10
c) 23R<10
d) 22R210​

Answer 1

Given:

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

$(0 < \alpha < 180)$

should lie in between the angle 0 degrees to 180 degrees.

Case-1.

$\sf \alpha = 0^{\circ}$

vector formula

$\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha ) }$

$\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab}$

as cos 0 is 1.

$\sf R = a + b$

$\sf R = 6 + 4$

$\sf R = 10 \: units$

Case-2

$\sf \alpha = 180^{\circ}$

$\sf R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos( \alpha )}$

$\sf R = \sqrt{ {a}^{2} + {b}^{2} - 2ab}$

as cos 180 is -1.

$\sf R = a - b$

$\sf R = 6 - 4$

$\sf R = 2 \: units$

so, the resultant R will be in between these values.

Therefore, the resultant R will be in between these values.

Hence, option (c) is correct.

Answer 2

Answer:

crct ans

Explanation: