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  • Please Solve RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Fill in the blanks Question 14 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Fill in the blanks Question 14 Maths Textbook Solution.

Answers (1)

Answer : The required answer is 2

Hint :   The condition of coplanar is

            (\overrightarrow{a 2}-\overrightarrow{a 1}) \cdot(\overrightarrow{b 2} \times \overrightarrow{b 1})=0    -----1

Given :  \overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{a} 1}+\lambda \overrightarrow{\mathrm{b} 1} \text { and } \overrightarrow{\mathrm{r}}=2 \overrightarrow{\mathrm{a} 2}+\lambda \overrightarrow{\mathrm{b} 2}        ------2

Solution :  From Eq.1 and Eq.2

                 \begin{aligned} &(\overrightarrow{a 2}-\overrightarrow{a 1}) \cdot(\overrightarrow{b 2} \times \overrightarrow{b 1})=0 \\ & \end{aligned}

                 (2 \overrightarrow{a 2}-\overrightarrow{a 1}) \cdot\lfloor{b 2} \times \overrightarrow{b 1})=0

                 \begin{gathered} 2(\overrightarrow{a 2} \cdot(\overrightarrow{b 2} \times \overrightarrow{b 1}))-\overrightarrow{a 1} \cdot(\vec{b} 2 \times \overrightarrow{b 1})=0 \\ \end{gathered}   

                 2 \overrightarrow{a 2} \cdot(\overrightarrow{b 2} \times \overrightarrow{b 1})-\overrightarrow{a 1} \cdot(\overrightarrow{b 2} \times \overrightarrow{b 1})=0      -------3

                    Now  \frac {[\overrightarrow{a 1}\overrightarrow{b 1}\overrightarrow{b2} ]}{[\overrightarrow{a 2}\overrightarrow {b1}\overrightarrow{b2} ]} = \frac{\overrightarrow{a1}.\left ( \overrightarrow{b1}\times \overrightarrow{b2}\right )}{\overrightarrow{a2}.\left ( \overrightarrow{b1}\times \overrightarrow{b2}\right )}                    [Using scalar triple formula]

                                             = \frac{2\overrightarrow {a2}\cdot \left ( \overrightarrow{b1}\times\overrightarrow{b2} \right )}{\overrightarrow {a2}\cdot \left ( \overrightarrow{b1}\times\overrightarrow{b2} \right )}                  Substituting the values in Numerator

                                             = 2

                                            

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