Question

If vectors A and B are such that |A+B| =| A| = |BI,
then |A - B |may be equated to
​

Answer 1

From scalar product:

X⋅Y=|X||Y|cosαxy

|A+B|2

=|A+B||A+B|cos0

=(A+B)⋅(A+B)

=A2+B2these are equal+A⋅B+B⋅these commute

=2A2+2A⋅B

And:

|A+B|2=A2

⇒A⋅B=−12A2

Similarly:

|A−B|2

=2A2−2A⋅B

=2A

Answer 2

Answer:

$\sqrt{3}$|A|

Explanation: