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  • Need solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 11

Need solution for RD Sharma maths class 12 chapter 27 Straight Line in Space exercise Multiple choice question 11

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Answer: Correct answer is A.

Hint: Use vector dot product.

Given: x,y and z are 12, 4 and 3

Solution: Let the line segment be represented in vector form as \vec{a}=a_{1} \vec{\imath}+a_{2} \vec{\jmath}+a_{3} \vec{k}  vector along co-ordinate axes are\vec{i}, \vec{j}, \vec{k} vector along given that projection of \vec{a} \text { on } x-\text { axis is } 12, that with y-\text { axis is } 4  and

that with z-\text { axis is } 3.


\begin{aligned} &\Rightarrow \vec{a} \cdot \vec{l}=12 \\\\ &\Rightarrow a_{1}=12 \end{aligned}

Similarly a_{2}=4, a_{3}=3

\therefore \vec{a}=12 \vec{\imath}+4 \vec{\jmath}+3 \vec{k}

The line segment of the length |\vec{a}|=\sqrt{144+16+9} \Rightarrow 13  and the direction cosines of the line segment are <13, \frac{12}{13}, \frac{4}{13}, \frac{3}{13}>

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