# If the sum of two unit vectors is a unit vector, what is the magnitude of the difference of the two vectors?

##### 2 Answers

Unit vector: The vector whose magnitude is unity(1) is called unit vector.

#### Explanation:

Let ai+bj and ci+dj be the unit vectors.

From the defination,

*_**_*(1)

** _**____(2)

Add the above two vectors,

(ai+bj)+(ci+dj) =(a+c)i+(b+d)j*_*** _**(3)

Also given that,

The magnitude of equation(3) is also unity.

*_**_*** _**(4)

the magnitude of their difference is:?

THe difference of two unit vectors is

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is 1.73205

The magnitude (length) of the difference is

(Alternate method of seeing this).

#### Explanation:

For those more visually or geometrically oriented; consider the following diagram, noting that if the sum of two unit vectors is a unit vector then the 3 unit vectors can be combined into an equilateral triangle:

By extending the initial unit vector and dropping a perpendicular to that extension from the terminal point of the vector

we have a right triangle with sides:

So