The manganate ion (\({MnO_4^{2-}}\)) undergoes a disproportionation reaction in an acidic medium.
In this reaction:
Reaction:
\[ 2{MnO_4^{2-}} + 4{H^+} \rightarrow {MnO_4^-} + {Mn^{2+}} + 2{H_2O} \]
When potassium permanganate (\({KMnO_4}\)) is heated, it decomposes to form potassium manganate (\({K_2MnO_4}\)) and oxygen gas.
Reaction:
\[ 2{KMnO_4} \xrightarrow{\text{heat}} {K_2MnO_4} + {O_2} \]
This is a decomposition reaction that releases oxygen and forms a green manganate salt.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?