Direction vectors
${\bf r}_1 = 3{\bf i} - 4{\bf j} + 6{\bf k}$
${\bf r}_2 = -2{\bf i} + 4{\bf j} - 5{\bf k}$
${\bf r}_3 = -4{\bf i} + 5{\bf j} - 3{\bf k}$
Unit vectors
${\bf \lambda}_1 = \dfrac{3{\bf i} - 4{\bf j} + 6{\bf k}}{\sqrt{3^2 + 4^2 + 6^2}} = 0.384{\bf i} - 0.512{\bf j} + 0.768{\bf k}$
${\bf \lambda}_2 = \dfrac{-2{\bf i} + 4{\bf j} - 5{\bf k}}{\sqrt{2^2 + 4^2 + 5^2}} = -0.298{\bf i} + 0.596{\bf j} - 0.745{\bf k}$
${\bf \lambda}_3 = \dfrac{-4{\bf i} + 5{\bf j} - 3{\bf k}}{\sqrt{4^2 + 5^2 + 3^2}} = -0.566{\bf i} + 0.707{\bf j} - 0.424{\bf k}$
Forces in rectangular form
${\bf F} = F{\bf \lambda}$
${\bf F}_1 = 300(0.384{\bf i} - 0.512{\bf j} + 0.768{\bf k}) = 115.2{\bf i} - 153.6{\bf j} + 230.4{\bf k} ~ \text{lb}$
${\bf F}_2 = 400(-0.298{\bf i} + 0.596{\bf j} - 0.745{\bf k}) = -119.2{\bf i} + 238.4{\bf j} - 298{\bf k} ~ \text{lb}$
${\bf F}_3 = 200(-0.566{\bf i} + 0.707{\bf j} - 0.424{\bf k}) = -113.2{\bf i} + 141.4{\bf j} - 84.8{\bf k} ~ \text{lb}$
Resultant
${\bf R} = {\bf F}_1 + {\bf F}_2 + {\bf F}_3$
Sum up the coefficients of i, j and k
${\bf R} = -117.2{\bf i} + 226.2{\bf j} -152.8{\bf k} ~ \text{lb}$ answer
Calculator Operations Using VECTOR Mode
For CASIO fx-991ES Plus
