Question

The angle between two unit Vectors is what in case of Vector Addition?
A. 90
B. 60
C. 180
D. 120​

Answer 1

$\underline{\green{\mathfrak{Answer:-}}}$

(D) 120°

$\underline{\green{\mathfrak{Explanation:-}}}$

Given

unit vectors

To Find

Angle between them in case of vector addition

Solution:

As we know

Magnitude of unit vectors = 1

By the identity

$\boxed{\red{r = \sqrt{{a}^{2}+{b}^{2}+2ab cos \theta}}}$

Here

r = a = b = 1

Φ = ??

On putting values

$\mathsf{1 = \sqrt{{1}^{2}+{1}^{2}+2(1)(1) cos \theta}}$

$\mathsf{{1}^{2} = 1+1+2 cos \theta}$

$\mathsf{1 = 2+2 cos \theta}$

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

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

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

$\boxed{\purple{\theta = 120 \degree}}$

Hence, angle between the unit vectors = 120°

$\bold{\pink{NOTE:-}}$

small letters (a,b,r) represents MAGNITUDE of the vectors

Answer 2

Answer;

Option D

Prove

Given

Angle between two unit vectors= 120°

Resultant = 35 N

Also we Know that

(i)Vector addition of two unit vector is a unit vector.

$\hat{a} + \hat{b} = \hat{c}$

(ii) Resultant identity

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

(iii) Value of a unit Vector is 1.

According to Question

$= > R = \sqrt{ {a}^{2} + {b}^{2} + 2ab \cos \theta } \\ = > 1 = \sqrt{ {(1)}^{2} + {(1)}^{2} + 2 \times 1 \times 1 \cos \theta } \\ = > 1 = \sqrt{1 + 1 + 2 \cos \theta } \\ = > 1= 2 + 2 \cos \theta \\ = > - 1 = 2 \cos \theta \\ = > \cos \theta = > - \frac{ 1}{2} \\ = > \boxed{ \theta = 120 \degree}$

Hence Proved