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  • The distance of the point from the plane measured parallel to a line,

The distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to a line, whose direction ratios are 2,3,-6 is :
Option: 1 2
Option: 2 5
Option: 3 3
Option: 4 1

Answers (1)

best_answer


The equation of line passing through A(1,-2,3) and parallel to line with direction ratios 2,3,-6 will be \vec{r}= \hat{i}-2\hat{j}+3\hat{k}+\lambda \left ( 2\hat{i}+3\hat{j}-6\hat{k} \right )
Let this line cut the given plane at point B :
B\left ( 1+2\lambda ,-2+3\lambda ,3-6\lambda \right )
B\: lies\: on\: plane\: x-y+z-5= 0
\Rightarrow 1+2\lambda -\left ( -2+3\lambda \right )+3-6\lambda -5= 0
\Rightarrow \lambda = \frac{1}{7}
so \; co-ordinates \; \; of\; B\; are :\left ( \frac{9}{7},\frac{-11}{7},\frac{15}{7} \right )
Distance\, AB= \sqrt{\left ( 1-\left ( 1+2\lambda \right ) \right )^{2}+\left ( -2-\left ( -2+3\lambda \right ) \right )^{2}+\left ( 2-\left ( 3-6\lambda \right ) \right )^{2}}
                            = \sqrt{4\lambda ^{2}+9\lambda ^{2}+36\lambda ^{2}}
                            =7\left | \lambda \right |= 7\times \frac{1}{7}= 1
option (1)

Posted by

Kuldeep Maurya

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