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  • Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 6

Provide solution for RD Sharma maths class 12 chapter 28 The Plane exercise multiple choice question 6

Answers (1)

Answer:

 Option (d).

Hint:

 See for co-planer.

Given:

 \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-0}{3} \text { and } \frac{x-0}{-2}=\frac{y-2}{-3}=\frac{z+1}{-1}

Solution:

We know, the two lines given as,

\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-0}{3} \text { and } \frac{x-0}{-2}=\frac{y-2}{-3}=\frac{z+1}{-1}

\begin{aligned} &\vec{b_1}=2\hat{i}-\hat{j}+3\hat{k}\\ &\vec{b_2}=-\hat{i}-3\hat{j}-\hat{k}\\ &=\begin{vmatrix} \hat{i} &\hat{j} &\hat{k} \\ 2 &-1 &3 \\ -1 &-3 &-1 \end{vmatrix}\\ &=-8\hat{i}-\hat{j}+5\hat{k} \end{aligned}

Lines passes through (1,-1,0)

\begin{aligned} &(x-x_1)a+(y-y_1)b+(z-z_1)c=0\\ &(x-1)(-8)+(y+1)(-1)+(z-0)5=0\\ &-8x+8-y-1+5z=0\\ &-8x-y+5z+7=0\\ &8x+y-5z-7=0 \end{aligned}

Hence, option a is correct

Posted by

Gurleen Kaur

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