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Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
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If $\vec{\text{r}}\cdot\vec{\text{a}}=0,\vec{\text{r}}\cdot\vec{\text{b}}=0,$ and $\vec{\text{r}}\cdot\vec{\text{c}}=0$ for some non-zero vector $\vec{\text{r}},$ then the value of $\vec{\text{a}}(\vec{\text{b}}\times\vec{\text{c}})$ is _______.
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Answer

If $\vec{\text{r}}\cdot\vec{\text{a}}=0,\vec{\text{r}}\cdot\vec{\text{b}}=0,$ and $\vec{\text{r}}\cdot\vec{\text{c}}=0$ for some non-zero vector $\vec{\text{r}},$ then the value of $\vec{\text{a}}(\vec{\text{b}}\times\vec{\text{c}})$ is 0.Solution:
Since, $\vec{\text{r}}$ is a non-zero vector, so we can say that $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are in a same plane.
$\vec{\text{a}}(\vec{\text{b}}\times\vec{\text{c}})=0$
[Since, angle between $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are zero i.e., $\theta=0]$

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