Question

Let the vectors `vec(a)` such `vec(b)` that `|veca|` = 3 and `|vecb| = sqrt(2)/3`, then `veca xx vecb` is a unit vector if the angle between `veca` and `vecb` is

पर्याय

• `pi/6`

• `pi/4`

• `pi/3`

• `pi/2`

Answer 1

`pi/4`

Explanation:

`veca xx vecb = |veca||vecb| sin theta * hatn`

or `|veca xx vecb| = |veca||vecb| sin theta`

Now, `|veca|` = 3, `|vecb| = sqrt(3)/3`

Also, `|veca xx vecb|` is a unit vector,

∴ `|veca xx vecb|` = 1

⇒ `|veca||vecb| sin theta` = 1

`3 xx sqrt(2)/3 sin theta` = 1

∴ `sin theta = 1/sqrt(2)`

∴ `theta = pi/4`