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Scalar Triple Product — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsScalar Triple Product2 Marks
Question
Write the value of $\big[\hat{\text{i}}+\hat{\text{j}}\hat{\text{j}}+\hat{\text{k}}\hat{\text{k}}+\hat{\text{i}}\big].$
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Answer

We have
$\big[\hat{\text{i}}+\hat{\text{j}}\hat{\text{j}}+\hat{\text{k}}\hat{\text{k}}+\hat{\text{i}}\big]=\big[\big(\hat{\text{i}}+\hat{\text{j}}\big)\times\big(\hat{\text{j}}+\hat{\text{k}}\big)\big].\big(\hat{\text{k}}+\hat{\text{i}}\big)$ $\big(\therefore\big[\vec{\text{a}}\vec{\text{ b }}\vec{\text{c}}\big]=\big(\vec{\text{a}}\times\vec{\text{b}}\big).\vec{\text{c}}\big)$
$=\big[\hat{\text{i}}\times\hat{\text{j}}+\hat{\text{i}}\times\hat{\text{k}}+\hat{\text{j}}\times\hat{\text{j}}+\hat{\text{j}}\times\hat{\text{k}}\big].\big(\hat{\text{k}}+\hat{\text{i}}\big)$
$=\big[\hat{\text{k}}-\hat{\text{j}}+\hat{\text{i}}\big].\big(\hat{\text{k}}+\hat{\text{i}}\big)$
$=\big[\big(\hat{\text{k}}.\hat{\text{k}}\big)+\big(\hat{\text{k}}.\hat{\text{i}}\big)-\big(\hat{\text{j}}.\hat{\text{k}}\big)-\big(\hat{\text{j}}.\hat{\text{i}}\big)+\big(\hat{\text{i}}.\hat{\text{k}}\big)+\big(\hat{\text{i}}.\hat{\text{i}}\big)\big]$
$=1+0-0-0+0+1=2$

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