For the figure given below, find the value of $x_{B A}, x_{C A}, x_{C B}, x_{A B}$ and $x_{A C}$ respectively where $x_{A B}$ represents position of $A$ with respect to $B$ .

4 m, 10 m, 6 m, - 4 m, - 10 m

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- 4 m, 10 m, 6 m, - 4 m, - 10 m

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4 m, - 10 m, 6 m, - 4 m, 10 m

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4 m, 10 m, - 6 m, 4 m, - 10 m

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Solution

The correct option is A $4 m, 10 m, 6 m, - 4 m, - 10 m$
Taking the position of A as origin and right direction as x-axis.
Position of $B$ w.r.t. $A$ ,
$(x_{B A} = x_{B} - x_{A} = 4 - 0 = 4 m)$
$x_{B A} = 4 m$
Position of $C$ w.r.t. $A$
$(x_{C A} = x_{C} - x_{A} = + 10 - 0 = 10 m)$
$x_{C A} = 10 m$
Position of $C$ w.r.t. $B$
$(x_{C B} = x_{c} - x_{B} = + 6 - 0 = 6 m)$
$x_{C B} = 6 m$
Position of $A$ w.r.t. $B$
$(x_{A B} = x_{A} - x_{B} = 0 - 4 = - 4 m)$
$x_{A B} = - 4 m$
Position of $A$ w.r.t. $C$
$(x_{A C} = x_{A} - x_{C} = 0 - 10 = - 10 m)$
$x_{A C} = - 10 m$

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