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  • Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.3 question 3

Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.3  question 3

Answers (1)

Answer:

\vec{r} \cdot \hat{\imath}=0, \quad \vec{r}, \hat{\jmath}=0, \quad \vec{r} . \hat{k}=0

Hint:

xy-plane?z=0,

yz-plane?x=0,

zx-plane?y=0,

Given:

Vector equations of co-ordinate plane.

Solution:

  1. Vector equ of XY-plane

        ∴cartesian equ of xy-plane


        \begin{aligned} &z=0 \\\\ &\Rightarrow 0 x+0 y+z=0 \\\\ &(x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot(0 \hat{\imath}+0 \hat{\jmath}+\hat{k})=0 \\\\ &\vec{r} \cdot \hat{k}=0[\vec{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k}] \end{aligned}

 

  1. Vector equ of yz-plane

        ∴cartesian equ of yz-plane


        \begin{aligned} &x=0 \\\\ &\Rightarrow(x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot(\hat{\imath}+0 \hat{\jmath}+0 \hat{k})=0 \\\\ &\Rightarrow \vec{r} \cdot \hat{\imath}=0 \end{aligned}

 

  1. Vector equ of xz-plane

          cartesian equ of xz-plane ∴y=0


            \begin{aligned} &y=0 \\\\ &\Rightarrow(x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot(0 \hat{\imath}+\hat{\jmath}+0 \hat{k})=0 \\\\ &\Rightarrow \vec{r} \cdot \hat{\jmath}=0 \end{aligned}

The vector equation of co-ordinate plane is

\vec{r} \cdot \hat{\imath}=0, \quad \vec{r} \cdot \hat{\jmath}=0, \quad \vec{r} \cdot \hat{k}=0

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