Question

Let a and b be two unit vectors and \thetais the angle between them. If a+b is also a unit vector, then what is the measure of \theta in radians? \theta=\frac{\pi}{4} \theta=\frac{\pi}{3} \theta=\frac{\pi}{2} \the=\frac{2\pi}{3}

Answer 1

Answer:

2π/3

Step-by-step explanation:

As a and b are unit vectors

let α be the angle between a and b

so, a = 1 and b = 1

given, a + b = 1

so, a^{2} + b^{2} + 2(a)(b)(cosα) = (a+b)^{2}

1^{2} + 1^{2} + 2(1)(1)(cosα) = 1^{2}

2cosα = -1

cosα = -1/2

so, α = 120°

now, 120° = 120 x π/180

so, α = 2π/3