Question

`veca, vecb` and `vecc` are perpendicular to `vecb + vecc, vecc + veca` and `veca + vecb` respectively and if `|veca + vecb|` = 6, `|vecb + vecc|` = 8 and `|vecc + veca|` = 10, then `|veca + vecb + vecc|` is equal to

Options

• `5sqrt(2)`

• 50

• `10sqrt(2)`

• 10

Answer 1

10

Explanation:

`|veca + vecb|` = 6 ⇒ `|veca|^2 + |vecb|^2 + 2veca.vecb` = 36  ......(i)

Similarly, `|vecb|^2 + |vecc|^2 + 2vecb.vecc` = 64  .....(ii)

And `|vecc|^2 + |veca|^2 + 2vecc.veca` = 100  ......(iii)

On adding equations (i), (ii) and (iii), we get

`|veca|^2 + |vecb|^2 + |vecc|^2 + (veca.vecb + vecb.vecc + vecc.veca)` = 100  ......(iv)

`|veca|^2 + |vecb|^2 + |vecc|^2` = 100 ......`(because veca.vecb + vecb.vecc + vecc.veca)`

Now, `|veca + vecb + vecc|^2 = |veca|^2 + |vecb|^2 + |vecc|^2 + 2(veca.vecb + vecb.vecc + vecc.veca)`

⇒ `|veca + vecb + vecc|^2` = 100

⇒ `|veca + vecb + vecc|` = 10