Question

if the sum of two unit vectors is a unit vector then the magnitude of difference is ​

Answer 1

Answer:

difference of the unit vector = √3

Explanation:

given that,

the sum of two unit vectors is a unit vector

let the two unit vectors be

since a and b are unit vectors so

|a| = 1

|b| = 1

a^ and b^

and the resultant be c^

according to the question,

a^ + b^ = c^

and,

we know that,

the magnitudes of the unit vector is 1

so,

here,

a^ + b^ = √(1² + 1² + 2(1)(1)cosф)

c^ = √(1 + 1 + 2cosф)

1² = 2 + 2cosф

2cosф = 1 - 2

2cosф = -1

cosф = -1/2

so,

ф = 120°

so,

angle between the two unit vectors = 120°

now,

difference of the same unit vector

a^ - b^ =

√(a² + b² - 2abcosф)

putting the values,

√(1² + 1² - 2(1)(1)cos120)

√(1 + 1 - 2 × -½)

= √(2 + 1)

= √3

so,

difference of the unit vector when the sum is a unit vector

= √3