Question

if resultant of two unit vectors a and b is also a unit vector, then magnitude of difference of a and B is​

Answer 1

Answer:

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Answer 2

Therefore the magnitude of difference between a and b is √3.

Given:

Unit vectors a and b and the resultant of these 2 unit vectors are also unit vectors.

To Find:

The magnitude of the difference between a and b.

Solution:

The given question can be solved as shown below.

Vector 'a', Vector 'b', and also the 'resultant of a and b' is also a unit vector.

So I a I = 1, I b I = 1 and I a + b I = 1

⇒  I a + b I² = I a I² + I b I² + 2I a I I b I cos θ

⇒ 1² = 1² + 1² + 2 × 1 × 1 × Cos θ

⇒ 1 = 2 + 2 Cos θ

⇒ Cos θ = -1/2 ⇒ θ = 120°

So the angle between 'a' and 'b' is 120°.

Now, I a - b I² = I a I² + I b I² - 2 I a I I b I cos θ

⇒ I a - b I² = 1 + 1 - 2 × 1 × 1 × (-1/2)

⇒ I a - b I² = 2 + 1 = 3

⇒ I a - b I = √3

Therefore the magnitude of difference between a and b is √3.

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