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  • Please Solve RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Very Short Answer Question 14 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 27 Straight Line in Space Exercise Very Short Answer Question 14 Maths Textbook Solution.

Answers (1)

Answer:

Required answer is  \left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{b}_{1} \times \vec{b}_{2}\right)=0

Hint:

Use formula  d=\left|\frac{\left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{b}_{1} \times \vec{b}_{2}\right)}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\right|

Given:

\vec{r}=\vec{a}_{1}+\lambda \vec{b}_{1} \text { And } \vec{r}=\vec{a}_{2}+\mu \vec{b}_{2}

Solution:

The shortest distance between the lines  \vec{r}=\vec{a}_{1}+\lambda \vec{b}_{1} \text { And } \vec{r}=\vec{a}_{2}+\mu \vec{b}_{2}    is given by

d=\left|\frac{\left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{b}_{1} \times \vec{b}_{2}\right)}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\right|

For the lines to be intersecting,  d=0

\left|\frac{\left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{b}_{1} \times \vec{b}_{2}\right)}{\left|\vec{b}_{1} \times \vec{b}_{2}\right|}\right|= 0

\left(\vec{a}_{2}-\vec{a}_{1}\right) \cdot\left(\vec{b}_{1} \times \vec{b}_{2}\right)=0

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