Solve [(-71/31+5/2)i+(82/31-2)j+(-32/31-frac{1}{2})k]

$$[ ( - \frac { 71 } { 31 } + \frac { 5 } { 2 } ) i + ( \frac { 82 } { 31 } - 2 ) j + ( - \frac { 32 } { 31 } - \frac { 1 } { 2 } ) k ]$$

Evaluate

$$\frac{20j}{31}-\frac{95k}{62}+\frac{13}{62}i$$

Solution Steps

Least common multiple of 31 and 2 is 62. Convert -\frac{71}{31} and \frac{5}{2} to fractions with denominator 62.

$$\left(-\frac{142}{62}+\frac{155}{62}\right)i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Since -\frac{142}{62} and \frac{155}{62} have the same denominator, add them by adding their numerators.

$$\frac{-142+155}{62}i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Add -142 and 155 to get 13.

$$\frac{13}{62}i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Convert 2 to fraction \frac{62}{31}.

$$\frac{13}{62}i+\left(\frac{82}{31}-\frac{62}{31}\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Since \frac{82}{31} and \frac{62}{31} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{62}i+\frac{82-62}{31}j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Subtract 62 from 82 to get 20.

$$\frac{13}{62}i+\frac{20}{31}j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Least common multiple of 31 and 2 is 62. Convert -\frac{32}{31} and \frac{1}{2} to fractions with denominator 62.

$$\frac{13}{62}i+\frac{20}{31}j+\left(-\frac{64}{62}-\frac{31}{62}\right)k$$

Since -\frac{64}{62} and \frac{31}{62} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{62}i+\frac{20}{31}j+\frac{-64-31}{62}k$$

Subtract 31 from -64 to get -95.

$$\frac{13}{62}i+\frac{20}{31}j-\frac{95}{62}k$$

Expand

$$\frac{20j}{31}-\frac{95k}{62}+\frac{13}{62}i$$

Solution Steps

Least common multiple of 31 and 2 is 62. Convert -\frac{71}{31} and \frac{5}{2} to fractions with denominator 62.

$$\left(-\frac{142}{62}+\frac{155}{62}\right)i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Since -\frac{142}{62} and \frac{155}{62} have the same denominator, add them by adding their numerators.

$$\frac{-142+155}{62}i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Add -142 and 155 to get 13.

$$\frac{13}{62}i+\left(\frac{82}{31}-2\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Convert 2 to fraction \frac{62}{31}.

$$\frac{13}{62}i+\left(\frac{82}{31}-\frac{62}{31}\right)j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Since \frac{82}{31} and \frac{62}{31} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{62}i+\frac{82-62}{31}j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Subtract 62 from 82 to get 20.

$$\frac{13}{62}i+\frac{20}{31}j+\left(-\frac{32}{31}-\frac{1}{2}\right)k$$

Least common multiple of 31 and 2 is 62. Convert -\frac{32}{31} and \frac{1}{2} to fractions with denominator 62.

$$\frac{13}{62}i+\frac{20}{31}j+\left(-\frac{64}{62}-\frac{31}{62}\right)k$$

Since -\frac{64}{62} and \frac{31}{62} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13}{62}i+\frac{20}{31}j+\frac{-64-31}{62}k$$

Subtract 31 from -64 to get -95.

$$\frac{13}{62}i+\frac{20}{31}j-\frac{95}{62}k$$