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  • Please Solve RD Sharma Class 12 Chapter 28 The Plane Exercise 28 .11 Question 11 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 28 The Plane Exercise 28.11 Question 11 Maths Textbook Solution.

Answers (1)

Answer:

            \overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})+\mathrm{k}((2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}))

Hint: Use properties of plane

Given: Point (1,-1,2)  and plane  2 x-y+3 z-5=0

Solution: Equation of line passing through \vec{a}  and  \vec{b}  is given by  \vec{r}=\vec{a}+k \vec{b}              ……………. (1)

Given that the line passes through  (1,-1,2) \text { is } \vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+k \vec{b}                …………….. (2)

Since, line (1) is perpendicular to the plane  2 x-y+3 z-5=0

So, normal to plane is parallel to the line.

In vector form,

            \overrightarrow{\mathrm{b}}=\mathrm{m}(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}})  as, is any scalar.

Thus, the equation of required line,

            \overrightarrow{\mathrm{r}}=(\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}})+\mathrm{k}((2 \hat{\mathbf{i}}-\hat{\mathrm{j}}+3 \hat{\mathrm{k}}))

 

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