Question

25. The resultant of two vectors of magnitudes 3A and
2A is R. If the first vector is doubled, then the
magnitude of resultant is also doubled. The angle
between two vectors is
(1) 60°
12) 120
(3) 90°
(4) 180
miven
by​

Answer 1

Answer:

The angle  between two vectors is 120°

(2) is correct option.

Explanation:

Given that,

Magnitude of first vector = 3A

Magnitude of second vector = 2 A

The resultant is

$R^2=(3A)^2+(2A)^2+2\times3A\times2A\cos\theta$.....(I)

If the first vector is doubled, then the  magnitude of resultant is also doubled.

The new resultant is,

$(2R)^2=(6A)^2+(2A)^2+2\times6A\times2A\cos\theta$.....(II)

We need to calculate the  angle  between two vectors is

divided equation (I) by equation (II)

$\dfrac{R^2}{4R^2}=\dfrac{9A^2+4A^2+12A^2\cos\theta}{36A^2+4A^2+24A^2\cos\theta}$

$\dfrac{1}{4}=\dfrac{13+12\cos\theta}{40+24\cos\theta}$

$\40+24\cos\theta=52+48\cos\theta$

$-12=24\cos\theta$

$\cos\theta=-\dfrac{1}{2}$

$\theta=120^{\circ}$

Hence, The angle  between two vectors is 120°