Question

If `|bara|` = 3, `|barb|` = 5 and `|bara + barb|` = 4 then `|bara - barb|` is equal to ______.

विकल्प

• 2

• `4sqrt(13)`

• `2sqrt(13)`

• `sqrt(13)`

Answer 1

If `|bara|` = 3, `|barb|` = 5 and `|bara + barb|` = 4 then `|bara - barb|` is equal to `underlinebb(2sqrt(13))`.

Explanation:

`|bara + barb|^2 = (bara + barb)*(bara + barb)`

(4)² = `|bara|^2 + 2bara*barb + |barb|^2`

16 = `2bara*barb + 34`

∴ `2bara*barb` = – 18   ...(1)

Now `|bara - barb|^2 = |bara|^2 - 2bara*barb + |barb|^2`

= 9 + 18 + 25   ...(Using (1))

= 52

∴ `|bara - barb| = sqrt(52) = 2sqrt(13)`