Question

|a|=3 |b|=4 |a+b|=5 then calculate the value of |a-b|​

Answer 1

Answer:

|a-b|^2=(a-b)•(a-b)

= a^2-2a•b+b^2

= |a|^2-2a•b+|b|^2

= 3^2-2a•b+4^2

=9+16-2a•b

=25-2a•b........eq1

Now,

|a+b|^2=(a+b)•(a+b)

5^2 = |a|^2+|b|^2+2a•b

25 = 25+2a•b

2a•b= 0

Now putting the value of 2a•b in eq1

we get |a-b|^2=25

|a-b|=5