Question

lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______ 

पर्याय

• `3/2`

• 0

• `(3sqrt3)/2`

• 3

Answer 1

lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = `underline((3sqrt3)/2)`.

Explanation:

Since, `overlinea + overlineb + overlinec = 0`,

∴ `overlinea xx overlineb = overlineb xx overlinec = overlinec xx overlinea`

`|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea| = 3|overlinea xx overlineb|`

= `3|overlinea| |overlineb| sin  pi/3`

= `(3sqrt3)/2`