Question

29. If two forces A and B are such that A+
B = Čand A+ B2 = C2 then the angle
between A and B is
a) 0° b) 30° C) 90° d) 180°​

Answer 1

Basics to be known for the question:

Triangle law of vector addition: If 2 vectors
Pythagoras theorem
If A is a vector quantity then A^2 = |A|^2
Now, coming to the question,

Given, A + B= C, A,B and C are vectors

This implies, they must follow Triangle law of vector addition, and would look like


Secondly, 2=||2
A
2
=
|
A
|
2
(=a in the pic above) as said earlier.

Lastly, Since a, b and c are sides of the triangle ABC above, thus

Given 2+2=2
a
2
+
b
2
=
c
2
, using Pythagoras theorem We can say that the triangle is a right angled triangle, right angled at B

Hence angle at B or the angle between A and B is a right angle or 90 degrees or π /2 radians, hence option b is the right answer.