Question

If | f1 X f2 |= F1 . F2 then | f1 + f2 | = ?

Answer 1

✪ᴀɴsᴡᴇʀ✪

$\green{\boxed{ |\vec{F}_1 + \vec{F}_2| = \sqrt{(F_1)^2 + (F_2)^2 + \sqrt{2} F_1F_2}}}$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Here

$\to |\vec{F}_1\times \vec{F}_2| = \vec{F}_1.\vec{F}_2$

If angle between $F_1, F_2$ is $\theta$

$\to F_1F_2sin(\theta) = F_1F_2cos(\theta)$

$\to sin(\theta) = cos(\theta)$

$\to tan(\theta) = 1$

$\to \theta = 45^o$

So,

$\to |\vec{F}_1 + \vec{F}_2|$

$= \sqrt{(F_1)^2 + (F_2)^2 + 2F_1F_2cos(\theta)}$

$= \sqrt{(F_1)^2 + (F_2)^2 + 2F_1F_2cos(45^o)}$

$= \sqrt{(F_1)^2 + (F_2)^2 + 2F_1F_2 \frac{1}{\sqrt{2}} }$

$= \sqrt{(F_1)^2 + (F_2)^2 + \sqrt{2} F_1F_2}$