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  • Need solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 3

Need solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 3

Answers (1)

Answer: Correct Answer is A.

Hint: Use vector cross product.

 

Given:\frac{x-7}{2}=\frac{y+17}{-3}=\frac{z-6}{-1} \text { and } \frac{x+5}{1}=\frac{y+3}{2}=\frac{z-4}{-2}

 

Solution: The direction ratios of the given lines are proportional to 2,-3, 1 and 1,2,-2.

The given lines are parallel to the vectors

\Rightarrow \overrightarrow{b_{1}}=2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \operatorname{and} \overrightarrow{b_{2}}=\hat{\imath}+2 \hat{\jmath}-2 \hat{k}

Vector perpendicular to the given two lines is

\begin{aligned} &\Rightarrow \vec{b}=\overrightarrow{b_{1}} \times \overrightarrow{b_{2}} \\\\ &\Rightarrow\left|\begin{array}{ccc} \hat{\imath} & \hat{\jmath} & \hat{k} \\ 2 & -3 & 1 \\ 1 & 2 & -2 \end{array}\right| \\\\ &\Rightarrow 4 \hat{\imath}+5 \hat{\jmath}+7 \hat{k} \end{aligned}

Hence, the direction ratios of the line perpendicular to the given two lines are proportional to 4,5,7.

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