Question

A particle moves from position r1=3i+2j-6k to position r2=14i+13j-9k under the action of a force f=8i+2j+6k.Find the work done by the force
a) 50 units b) 75 units c) 125 units d) 155 units e) 200 units ​

Answer 1

$\huge \bold {\red {\underline{ \underline{\mathfrak{ANSWER}}}}} \red{ :}$

$\star \: \: \: \: \: \underline \blue{Given} \blue{:-}$

$\overrightarrow { r1 }= 3 \hat{i} + 2 \hat{j} - 6 \hat{k} \\ \overrightarrow { r2 }= 14 \hat{i} + 13 \hat{j} - 9 \hat{k} \\ \overrightarrow F = 8 \hat{i} + 2 \hat{j} + 6 \hat{k}$

$\star \: \: \: \: \: \underline \blue{Find} \blue{:-}$

WORK DONE BY FORCE F

$\star \: \: \: \: \: \underline \blue{Solution} \blue{:-}$

$w = \overrightarrow {F} • \overrightarrow{s}$

$w = (8 \hat{i} + 2 \hat{j} + 6 \hat{k}) (14 \hat{i} + 13 \hat{j} - 9 \hat{k} - 3 \hat{i} - 2 \hat{j} + 6 \hat{k}) \\ \longrightarrow w = (8 \hat{i} + 2 \hat{j} + 6 \hat{k}) (11 \hat{i} + 11 \hat{j} - 3 \hat{k}) \\ \longrightarrow \: w = (88+ 0+ 0 + 0 + 22 + 0 + 0 + 0 -18) \\ \longrightarrow \bold{\boxed{\mathfrak {w = 92}}}$

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