logo
or
search
upload

If a and b are unit vectors, then the greatest value of |a+b|+|a-b| is

Apne doubts clear karein ab Whatsapp par bhi. Try it now.
CLICK HERE

Watch 1000+ concepts & tricky questions explained!

6.2 K+ views | 3.2 K+ people like this

   
Share
Share

Answer Text

24`2sqrt2``sqrt2`

Answer :
C
Solution :
Let `theta` be an angle between unit vectors a and b. Then, `a.b =cos theta` <br> Now, `|a+b|^(2)=|a|^(2)+|b|^(2)+2a.b` <br> `=1+1+2xx1xx1xxcos theta` <br> `=2+2 cos theta=4 "cos"^(2) theta/2` <br> `implies |a+b|=2 "cos" theta/2` <br> and `|a-b|^(2)=|a|^(2)+|b|^(2)-2a.b` <br> `=2-2 cos theta=2 (2 "sin"^(2) theta/2)` <br> `|a-b|=2"sin" theta/2` <br> `:. |a+b|+|a-b|=2 ("cos" theta/2 +"sin"theta/2) le 2 sqrt(2)`

Related Answer
bottom open in app