Question

Three forces of magnitudes $1,2$ and $3$ dynes meet in a point and act along diagonals of three adjacent faces of a cube. The resultant force is?

• A. $114$ dynes
• B. $6$ dynes
• C. $5$ dynes
• D. None of the above

Answer 1

Answer: (C)

$5$ dynes

Three vectors meeting at a point are $i+j,j+k$ and $k+i$. Forces of $1,2$ and $3$ dynes are acting along these directions respectively, therefore resultant force.
$=\frac{i+j}{\sqrt{2}}+\frac{2(j+k)}{\sqrt{2}}+\frac{3(k+i)}{\sqrt{2}}$
$=\frac{1}{\sqrt{2}}(4i+3j+5k)$
$\therefore$ Magnitude $=\frac{5\sqrt{2}}{\sqrt{2}}=5$ dynes.