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  • Explain solution RD Sharma class 12 Chapter 27 Striaght Line in Space Exercise Very Short Answer question 17

Explain solution RD Sharma class 12 Chapter 27 Striaght Line in Space Exercise Very Short Answer question 17

Answers (1)

Answer:

Required answer is  \vec{r}=5 \hat{i}-4 \hat{j}+6 \hat{k}+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})

Hint:

Use properties of vector

Given:

\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}

Solution:

We have,

\frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}

The given line passes through the point  \left ( 5,-4,6 \right ) and has direction ratios proportional to  3,7,2

Vector equation of the given line passing through the point having position vector

\vec{a}=5 \hat{i}-4 \hat{j}+6 \hat{k}  and parallel to a vector  \vec{b}=3 \hat{i}+7 \hat{j}+2 \hat{k}  is

\begin{aligned} &\vec{r}=\vec{a}+\lambda \vec{b} \\ & \end{aligned}

\vec{r}=5 \hat{i}-4 \hat{j}+6 \hat{k}+\lambda(3 \hat{i}+7 \hat{j}+2 \hat{k})

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