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  • Explain solution RD Sharma class 12 Chapter 27 Striaght Line in Space Exercise Fill in the blanks question 18

Explain solution RD Sharma class 12 Chapter 27 Striaght Line in Space Exercise Fill in the blanks question 18

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Answer :   3 \hat{\imath}+4 \hat{\jmath}-7 \hat{k}+\lambda(-2 \hat{\imath}-5 \hat{\jmath}+13 \hat{k})

Hint : Use the vector equation

Given :     (3 , 4 , -7) and ( 1 , -1 , 6)

Solution : position vector of (3 , 4 , -7) is

                  \vec{a}=3 \hat{\imath}+4 \hat{\jmath}-7 \hat{k}

                  And position vector of ( 1 , -1 , 6) is

                  \vec{b}=\hat{\imath}-\hat{\jmath}+6 \hat{k}

                  Also,

                  The vector equation of a line which passes through two

                   Points whose position vectors are  \vec{a} \text { and } \vec{b}   is

                  \vec{r}=\vec{a}+\lambda(\vec{b}-\vec{a})

                    Hence , required equation of line is

           \begin{aligned} &\Rightarrow \vec{r}=3 \hat{\imath}+4 \hat{\jmath}-7 \hat{k}+\lambda[\hat{\imath}-\hat{\jmath}+6 \hat{k}-(3 \hat{\imath}+4 \hat{\jmath}-7 \hat{k})] \\ & \end{aligned}

           \Rightarrow \vec{r}=3 \hat{\imath}+4 \hat{\jmath}-7 \hat{k}+\lambda(-2 \hat{\imath}-5 \hat{\jmath}+13 \hat{k})

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