Question

if the sum of two unit vectors is also a unit vector then magnitude of their difference and angle between the two given unit vectors is

Answer 1

angle between two vector will be 120

Answer 2

The correct answer to the question is 120 degree.

CALCULATION:

We know that magnitude of a unit vector is one.

Let the two unit vectors are denoted as $\hat A\ and\ \hat B\ respectively$

Let the angle between them is $\theta$

As per the question, the sum of these two unit vectors is also a unit vector.

Let the resultant of these two vectors is denoted as $\hat R$.

From parallelogram law of vector addition, we know that-

                                                   $R^2=\ A^2+B^2+2ABcos\theta$

                                                  ⇒ $1^2=\ 1^2+1^2+2\times 1\times 1\times cos\theta$

                                                  ⇒ $1=2+2cos\theta$

                                                  ⇒ $-1=\ 2cos\theta$

                                                  ⇒ $cos\theta=\ -\frac{1}{2}$

                                                  ⇒ $\theta=\ 120^{0}$    (∵ $cos120=\ -\frac{1}{2}$ )

                                                                                          [ans]