Question

Calculate the magnitude of the resultant of 2-unit vectors, when they are inclined to each other at 0°​

Answer 1

Given,

The angle between two unit vectors = 0°

a=1 , b=1

To Find,

The magnitude of the resultant between 2 unit vectors at an angle of 0°

Solution,

R = $\sqrt{a^{2} +b^{2} +2abCosΘ}$

According to the given question

cos0° = 1

Therefore,

R= $\sqrt{1^{2} +1^{2} +2cos0}$

R=$\sqrt{4\\}$

R=2

Hence, the magnitude of the resultant ​is 2.

Answer 2

Magnitude of the resultant of 2 unit vectors when they are inclined to each other at 0°​  is 2  units

Given:

2 unit Vectors inclined to each other at 0°​

To Find:

Magnitude of the resultant

Solution:

Magnitude of Resultant of Two vectors with magnitude A and B is given by :

$R=\sqrt{A^2+B^2+2AB\cos\theta}$

where θ is the angle between Vectors

Unit Vectors has magnitude unity  i.e 1

Step 1:

Substitute A = 1 , B = 1 , θ = 0°

$R=\sqrt{1^2+1^2+2(1)(1)\cos 0^{\circ}}$

$R=\sqrt{1+1+2\cos 0^{\circ}}$

$R=\sqrt{2+2\cos 0^{\circ}}$

Step 2:

Use cos0° = 1 and calculate

$R=\sqrt{2+2(1)}$

$R=\sqrt{2+2}$

$R=\sqrt{4}$

$R=2$

Hence magnitude of the resultant of 2 unit vectors when they are inclined to each other at 0°​  is 2  units