Answer
$$(0.15k+0.6i)(-5.2i-12j+20.8k)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(0.15k+0.6i)(-5.2i-12j+20.8k)& \xlongequal{ }(0k+0i)(-5i-12j+20k) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}0ik+0jk+0k^2+0i^2+0ij+0ik \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{0ik}0jk0k^20i^20ij \cancel{0ik} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}0\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{0k0i}\right) $ by each term in $ \left( -5i-12j+20k\right) $. $$ \left( \color{blue}{0k0i}\right) \cdot \left( -5i-12j+20k\right) = \cancel{0ik}0jk0k^20i^20ij \cancel{0ik} $$ |
| ② | Combine like terms: $$ \, \color{blue}{ \cancel{0ik}} \,0jk0k^20i^20ij \, \color{blue}{ \cancel{0ik}} \, = 0 $$ |
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