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Scalar Triple Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Triple Product2 Marks
Question
Evaluate the following:
$\big[\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{j}}\hat{\text{k}}\hat{\text{i}}\big]+\big[\hat{\text{k}}\hat{\text{i}}\hat{\text{j}}\big]$
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Answer

We have,
$\big[\hat{\text{i}}\hat{\text{ j}}\hat{\text{ k}}\big]+\big[\hat{\text{j}}\hat{\text{ k}}\hat{\text{ i}}\big]+\big[\hat{\text{k}}\hat{\text{i}}\hat{\text{j}}\big]$
$=(\hat{\text{i}}\times\hat{\text{j}}).\hat{\text{k}}(\hat{\text{j}}\times\hat{\text{k}}).\hat{\text{i}}+(\hat{\text{k}}\times\hat{\text{i}}).\hat{\text{j}}$
$=\hat{\text{k}}.\hat{\text{k}}+\hat{\text{i}}.\hat{\text{i}}+\hat{\text{j}}.\hat{\text{j}}$
$=1+1+1$
$=3$
Therefore, $\big[\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{j}}\hat{\text{k}}\hat{\text{i}}\big]+\big[\hat{\text{k}}\hat{\text{i}}\hat{\text{j}}\big]=3$

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