Find the c value and give a step by step explanation

1.	Find the c value and give a step by step explanation
Answer» $\blue{\bold{\underline{\underline{Answer:}}}}$ $\green{\tt{\therefore{Value\:of\:c=6}}}$ $\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$ $\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt: \implies Force(F) = (3 \hat{i} - 2 \hat{j} + \hat{k}) \: N \\ \\ \tt: \implies Displacement(s) = (2 \hat{i} - 2 \hat{j} + c \hat{k} ) \: m\\ \\ \tt: \implies Work \: Done = 16 \: J \\ \\ \red{\underline \bold{To \: find :}} \\ \tt: \implies Value \: of \: c =?$ • ACCORDING to given QUESTION : $\bold{As \: we \: know \: that} \\ \tt: \implies Work \: Done = Force \times Displacement \\ \\ \tt: \implies 16 = (3 \hat{i} - 2 \hat{j} + \hat{k}) \times (2 \hat{i} - 2 \hat{j} + c \hat{k} ) \\ \\ \tt: \implies 16 = (3 \hat{i} \times 2 \hat{i}) + ( - 2 \hat{j} \times - 2 \hat{j}) + ( \hat{k} \times c \hat{k}) \\ \\ \tt \circ \: \: \: \hat{i} \times \hat{i} = 1 \\ \\ \tt \circ \: \: \: \hat{j} \times \hat{j} = 1 \\ \\ \tt \circ \: \: \: \hat{k} \times \hat{k} = 1 \\ \\ \tt: \implies 16 = 6 + 4 + c \\ \\ \tt: \implies 16 = 10 + c \\ \\ \tt: \implies c = 16 - 10 \\ \\ \green{\tt: \implies c = 6} \\ \\ \green{\tt \therefore Value \: of \: c \: is \: 6}$

Answer»

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:c=6}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{<klux>GIVEN</klux> :}} \\ \tt: \implies Force(F) = (3 \hat{i} - 2 \hat{j} + \hat{k}) \: N \\ \\ \tt: \implies Displacement(s) = (2 \hat{i} - 2 \hat{j} + c \hat{k} ) \: m\\ \\ \tt: \implies Work \: Done = 16 \: J \\ \\ \red{\underline \bold{To \: find :}} \\ \tt: \implies Value \: of \: c =?$

• ACCORDING to given QUESTION :

$\bold{As \: we \: know \: that} \\ \tt: \implies Work \: Done = Force \times Displacement \\ \\ \tt: \implies 16 = (3 \hat{i} - 2 \hat{j} + \hat{k}) \times (2 \hat{i} - 2 \hat{j} + c \hat{k} ) \\ \\ \tt: \implies 16 = (3 \hat{i} \times 2 \hat{i}) + ( - 2 \hat{j} \times - 2 \hat{j}) + ( \hat{k} \times c \hat{k}) \\ \\ \tt \circ \: \: \: \hat{i} \times \hat{i} = 1 \\ \\ \tt \circ \: \: \: \hat{j} \times \hat{j} = 1 \\ \\ \tt \circ \: \: \: \hat{k} \times \hat{k} = 1 \\ \\ \tt: \implies 16 = 6 + 4 + c \\ \\ \tt: \implies 16 = 10 + c \\ \\ \tt: \implies c = 16 - 10 \\ \\ \green{\tt: \implies c = 6} \\ \\ \green{\tt \therefore Value \: of \: c \: is \: 6}$