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  • Need solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 14

Need solution for RD sharma maths class 12 chapter 23 Scalar or dot product exercise Fill in the blanks question 14

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\left | \vec{r} \right |^{2}Hint:

               Squaring both sides

Given:

For any vector \left ( r.\hat{i} \right )^{2}+ \left ( r.\hat{j} \right )^{2}+\left ( r.\hat{k} \right )^{2}=___________

Solution:

\begin{aligned} &|r|=x \hat{\imath}+y \hat{\jmath}+z \hat{k} \\ &|\vec{r}|=\sqrt{x^{2}+y^{2}+z^{2}} \\ &|\vec{r}|^{2}=x^{2}+y^{2}+z^{2} \\ \end{aligned}

\begin{aligned} (r \cdot \hat{\imath})^{2}+(r \cdot \hat{\jmath})^{2}+(r \cdot \hat{k})^{2}=((x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot \hat{\imath})^{2}+((x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot \hat{\jmath})^{2}+((x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot \hat{k})^{2} \\ \end{aligned}

\begin{aligned} =x^{2}+y^{2}+z^{2} \\ (r \cdot \hat{\imath})^{2}+(r \cdot \hat{\jmath})^{2}+(r \cdot \hat{k})^{2}=x^{2}+y^{2}+z^{2}=|\vec{r}|^{2} \end{aligned}

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