The distance of the point (1,-2,3) from the plane x-y+z=5 measured parallel to a line, who…

Question

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

Accepted Answer

$$(1 + 2\lambda ) + 2 - 3\lambda  + 3 - 6\lambda  = 5$$

$$ \Rightarrow 6 - 7\lambda  = 5 \Rightarrow \lambda  = {1 \over 7}$$

so, $$P = \left( {{9 \over 7}, - {{11} \over 7},{{15} \over 7}} \right)$$

$$AP = \sqrt {{{\left( {1 - {9 \over 7}} \right)}^2} + {{\left( { - 2 + {{11} \over 7}} \right)}^2} + {{\left( {3 - {{15} \over 7}} \right)}^2}} $$

$$AP = \sqrt {\left( {{4 \over {49}}} \right) + {9 \over {49}} + {{36} \over {49}}}  = 1$$

Solutions · 1