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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 28 The Plane Exercise 28.13 Question 19 Sub Question 1 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 28 The Plane  Exercise 28.13 Question 19 Sub Question 1 Maths Textbook Solution.

Answers (1)

Answer:    \sqrt{3} units

Hint: use vector cross products

Given: \vec{r}=\left ( i+j \right )+\lambda \left ( i+2j-k \right )

Solution: equation of given line is

               \vec{r}=\left ( i+j \right )+\lambda \left ( i+2j-k \right )  and \vec{a}=\vec{r}+\vec{\lambda b}...................(i)

               where

               \vec{a}=i+j

                 \vec{a}=i+2j-k

Again:  \vec{r}=\left ( i+j \right )+\lambda \left ( i+2j-k \right )

           \begin{aligned} &\overline{a^{n}}=(i+j)+u(-i+j-2 k) \\ &=\overline{a^{n}}+\bar{u}^{\bar{b}} \\ \end{aligned}

Where \begin{aligned} &\overline{a^{1}}=(i+j) \\ &\vec{b}=-i+j-2 k \end{aligned}

The vector equation of the plane containing the line (i) and (ii) is given by            

             \begin{aligned} &\vec{b} x \bar{b}^{\overline{1}}=\left(\begin{array}{ccc} i & j & k \\ 1 & 2 & -1 \\ -1 & 1 & -2 \end{array}\right) \\ &i(-4+1)-j(-2-1)+k(1+2)=3 i+3 j+3 k \end{aligned}

 

                

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