Discussion Forum

If the magnitude  of a,b and a+b  are respectively 3,4 and 5.then the magnitude of (a-b) is

Answer:

Explanation:

We have |a|=3,|b|=4 and |a+b|=5

 Since,        |a+b|=5

$\therefore$    $|a+b|^{2}=25$

$\Rightarrow$      $(a+b).(a+b)=25$

$\Rightarrow$    $a.a+a.b+b+a+b.b=25$

$\Rightarrow$      $|a|^{2}+2a.b+|b|^{2}=25$    [$\therefore$ a.b=b.a]

$\Rightarrow$             $9+2 a.b+16=25$

$\Rightarrow$    $a.b=0$

Now, consider $|a-b|^{2}=(a-b)(a-b)$

= $a.a-a.b-b.a+b.b$

  = $|a|^{2}-2 a.b+|b|^{2}$     [$\because$ a.b=b.a]

 =$9-0+16=25$

$\Rightarrow$    $|a-b|=5$