Question

Let `veca, vecb, vecc` be three vectors of magnitudes 3, 4 and 5 respectively. If each one is petpendicular to the sum of the other two vectors, then `|veca + vecb + vecc|` =

विकल्प

• 5

• `3sqrt(2)`

• `5sqrt(2)`

• 12

Answer 1

`5sqrt(2)`

Explanation:

We have `|veca|` = 3, `|vecb|` = 4 and `|vecc|` = 5.

It is given that `veca ⊥ (vecb + vecc), vecb ⊥ (vecc + veca)` and `vecc ⊥ (veca + vecb)`

⇒ `veca.(vecb + vecc)` = 0, `vecb. (vecc + veca)` = 0, `vecc.(veca + vecb)` = 0

⇒ `veca . vecb + veca  . vecc` = 0, `vecb . vecc + vecb . veca` = 0, `vecc . veca + vecc. vecb` = 0

Adding all these, we get, `2(veca . vecb + vecb . vecc + vecc . veca)` = 0

⇒ `veca . vecb + vecb . vecc + vecc . veca` = 0

Now, `|veca + vecb + vecc|^2 = |veca|^2 + |vecb|^2 + |vecc|^2 + 2(veca . vecb + vecb . vecc + vecc . veca)` = 3² + 4² + 5² + 0 = 50

⇒ `|veca + vecb + vecc| = sqrt(50) = 5sqrt(2)`.