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  • Please solve RD Sharma class 12 chapter 27 Straight Line in Space exercise Multiple choice question 9 maths textbook solution

Please solve RD Sharma class 12 chapter 27 Straight Line in Space exercise Multiple choice question 9 maths textbook solution

Answers (1)

Answer: Correct answer is A.

Hint: Use properties of vector cosines.

Given: Direction ratio is proportional to 1,-3, 2

Solution: If the direction ratios of a line are proportional to 1,-3, 2 then its direction cosines are also proportional to 1,-3, 2.

So let directional cosines be x,-3x,2x

Now, sum of the squares of directional cosines =1 (property)

\text { So, } x^{2}+9 x^{2}+4 x^{2}=1

\begin{aligned} &\Rightarrow x^{2}=\frac{1}{14} \\\\ &\Rightarrow x=\pm \frac{1}{\sqrt{14}} \end{aligned}

So, direction cosines can be \pm\left(\frac{1}{\sqrt{14}} \hat{\imath}-\frac{3}{\sqrt{14}} \hat{j}+\frac{2}{\sqrt{14}} \hat{k}\right)

So, the correct option is (A)

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