Question

the sum of unit vector is a unit vector.
find the difference of the unit vector.
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Answer 1

QUESTION:

the sum of unit vector is a unit vector. find the difference of the unit vector.

Answer:

Unit vector difference = √3

Explanation:

Given that,

the sum of unit vector is a unit vector.

let the two unit vector be a^ and b^

we know that,

magnitude of a unit vector is 1

so,

ACCORDING TO THE QUESTION ,

a^ + b^ = 1

1² = 1² + 1² + 2(1)(1)cosθ

1 = 1 + 1 + 2cosθ

2 + 2cosθ = 1

2cosθ = 1 - 2

2cosθ = -1

cosθ = -1/2

so,

θ = 120°

now,

we have,

a = 1

b = 1

θ = 1

a^ - b^

a² + b² - 2abcosθ

=> √(1² + 1² - 2(1)(1)cos120)

= √(1 + 1 - 2 × (-1)/2)

= √(2 - (-1))

= √(2 + 1)

= √3

so

If the sum of two unit vector is a unit vector then angle between them will 120°

and the difference if the unit vector will √3

Unit vector difference = √3