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  • Please solve RD Sharma class 12 chapter Straight Line in Space exercise 27.3 question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Straight Line in Space exercise 27.3 question 5 maths textbook solution

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Answer: The answer of the given question is (4,0,-1).

 

Hint: Equate the coefficient of vector equation of line.

 

Given: vector r=(\hat{\imath}+\hat{\jmath}-\hat{k})+\lambda(3 \hat{\imath}-\hat{\jmath}) \text { and vector } r=(4 \hat{\imath}-\hat{k})+\mu(2 \hat{\imath}+3 \hat{k})

 

Solution: General points on the lines are

(1+3 \lambda) \hat{\imath}+(1-\lambda) \hat{\jmath}-\hat{k} \text { and }(4+2 \mu) \hat{\imath}+(3 \mu-1) \hat{k}

Lines intersect if

\begin{aligned} &(1+3 \lambda)=(4+2 \mu)\\\\ &1-\lambda=0\\\\ &\text { and } 3 \mu-1=-1 \end{aligned}

From (ii) and (iii), \lambda=1, \mu=0

Substituting in equation (i)

Since,1+3(1)=4+2(0) is true.

Hence, the lines intersect.

Point of intersection is :4 \hat{\imath}-\hat{k} \text { or }(4,0,-1)

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