Force F^{\to} applied on a body is written asF^{\to} = (n^{\^}F^{\to}) n^{\^} + G^{\to}, where n^{\^} is a unit vector . The vector G^{\to} is equal to

Correct Answer is : (n^×F→)×n^

n ^{\^} \times (n ^{\^} \times F ^{\to})

(n ^{\^} \times F ^{\to})\times F ^{\to}\/| F ^{\to}|

(n ^{\^} \times F ^{\to})\times n ^{\^}

KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 37 of 120

Marks: +1, -0

Force

F↖{→}

applied on a body is written as

F↖{→} = (n↖{\^}F↖{→}) \;\; n↖{\^} + G↖{→}

, where

n↖{\^}

is a unit vector .
The vector

G↖{→}

is equal to

Solution:

(n ↖{\^} × F ↖{→})× n ↖{\^} =-[n ↖{\^} × (n ↖{\^} × F ↖{→})]

=-[n ↖{\^} (n ↖{\^} . F ↖{→})-F ↖{→}(n ↖{\^} . n ↖{\^} )

=[F ↖{→}-n ↖{\^}(n ↖{\^} . F ↖{→})]

=G↖{→}

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