Question

if the sum of two unit vector is a unit vector, than find the magnitude of their difference is ?​

Answer 1

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Answer 2

HEY MATE..!!

$\huge\boxed{\fcolorbox{blue}{white}{Answer:--}}$

As question said.... Sum of 2 unit vector is a unit vector..

▪️Lets call these 2 unit vectors as A and B vector.

This means,

✒️magnitude of A=1

✒️magnitude of B=1

✒️magnitude of A+B=1

Now as you may recall the formula we studied...

magnitude of (A+B)= sqrt(A2+B2+2ABcos(x))

Here x represents the angle between 2 vectors (A and B)

▪️Now plugging the values as

A=1

B=1

And A+B=1

▪️We can get cos (x) =-0.5

▪️And this means x=120 degrees

▪️Once part of the question over...

✍️For the second part...

✒️Subtracting 2 vectors say A and B in this case is same as adding A and - B

A-B=A + (-B)

✒️This means as we reverse the side of B.... B becomes -B

Now add - B to A

✒️Here actually the x will change from 120 to 60 degrees...

▪️As explained in the ATTACHMENT.

$\huge\boxed{\fcolorbox{blue}{white}{Attachment!!}}$

So

A+(-B) =sqrt(A2+B2+2ABcos(60))

= $\small\boxed{\fcolorbox{blue}{white}{Answer=}}$ √3

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