Question

Given that \[A + B + C = 0\]. Out of three vectors, two are equal in magnitude and the magnitude of the third vector is \[\sqrt 2 \] times that of either of the two having equal magnitude. Then. The angles between the vectors are given by. 

 A. \[30^\circ ,60^\circ ,90^\circ \] 

B. \[45^\circ ,45^\circ ,90^\circ \]

C. \[45^\circ ,60^\circ ,90^\circ \]

D. \[90^\circ ,135^\circ ,135^\circ \]

Answer 1

Hint: The above problem can be resolved by using the fundamentals of the polygon law of vector addition. The concepts and fundamental principles involved in the law are used to identify the polygon and the correct values of angles between the vectors are analysed.

Complete step-by-step answer

Given: The sum of vectors is, \[A + B + C = 0\].

We know that according to the polygon law, the sum of three vectors is zero only when the polygon is formed as a closed polygon or the triangle. As per the given condition the two vectors have the same magnitude and the third vector has the magnitude \[\sqrt 2 \] time that of either of the two vectors of same magnitude. Then the triangle so formed is known as the right angled triangle.

Then, the values of angles are given as,

Angle between the A and B is, \[\alpha  = 90^\circ \].

Angle between the B and C is, \[\beta  = 135^\circ \].

Angle between the A and C is, \[\gamma  = 135^\circ \]. 

Therefore, the angles between the vectors are \[90^\circ ,135^\circ ,135^\circ \]. And option D is correct.

Note: In order to resolve the given problem, one must be clear with the concepts and fundamental laws regarding the vector addition, along with some commonly used laws like Polygon laws and parallelogram laws. Moreover, to identify the correct values of angles between the vectors, one must know the identity of the type of polygon.