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Scalar Triple Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Triple Product2 Marks
Question
Evaluate the following:$\big[2\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{i}}\hat{\text{k}}\hat{\text{j}}\big]+\big[\hat{\text{k}}\hat{\text{j}}2\hat{\text{i}}\big]$
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Answer

We have,
$\big[2\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat {\text{i}}\hat{\text{k}}\hat{\text{j}}\big]+\big[\hat{\text{k}}\hat{\text{j}}2\hat{\text{i}}\big]\\=(2\hat{\text{i}}\times\hat{\text{j}}).\hat{\text{k}}+(\hat{\text{i}}\times\hat{\text{k}}).2\hat{\text{i}}$
$=2\hat{\text{k}}.\hat{\text{k}}+(-\hat{\text{j}}).\hat{\text{j}}+(-\hat{\text{i}}).2\hat{\text{i}}$
$=2-1-2$
$=-1$
Therefore, $\big[2\hat{\text{i}}\hat{\text{j}}\hat{\text{k}}\big]+\big[\hat{\text{i}}\hat{\text{k}}\hat{\text{j}}\big]+\big[\hat{\text{k}}\hat{\text{j}}2\hat{\text{i}}\big]=-1$

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