Vectors A and B have equal magnitude. In addition, the magnitude of their resultant is also equal to the magnitude of either of them. Then A and B are at an angle of

Question

Vectors A and B have equal magnitude. In addition, the magnitude of their resultant is also equal to the magnitude of either of them. Then A and B are at an angle of (A) 30° (B) 60° (C) 90° (D) 120°

Tardigrade Admin · Accepted Answer

It is observed graphically that for | A | = |B | = | R | θ has to be 120° Allter Using R2 = A2 + B2 + 2 AB cos θ where R = B = A, we get A2 = A2 + A2 + 2 A2 cos θ i.e. cos θ = - (1/2) i.e. θ = 1200

Q. Vectors A and B have equal magnitude. In addition, the magnitude of their resultant is also equal to the magnitude of either of them. Then A and B are at an angle of

30 $^{\circ}$

60 $^{\circ}$

90 $^{\circ}$

120 $^{\circ}$

It is observed graphically that for $∣ A ∣ = ∣ B ∣ = ∣ R ∣$ $θ$ has to be $12 0^{\circ}$ Allter Using $R^{2} = A^{2} + B^{2} + 2 A B cos θ$ where R = B = A, we get $A^{2} = A^{2} + A^{2} + 2 A^{2} cos θ$ i.e. $cos θ = - \frac{1}{2}$ i.e. $θ = 12 0^{0}$