Question

find the c value and give a step by step explanation​

Answer 1

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

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

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

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

• 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 2

Given ,

Force (f) = (3i - 2j + k) N

Displacement (s) = 2i - 2j + ck) m

Work done (w) = 16 J

We know that ,

work done is dot product or scalar product of force and displacement

$\boxed { \sf{Work \: done = f.s }}$

Thus ,

16 = (3i - 2j + k) . (2i - 2j + ck)

16 = 3(2) + (-2)(-2) + 1(c)

16 = 6 + 4 + c

16 = 10 + c

c = 6

★ The value of c is 6