Straight lines in 3D

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Question

If the foot of the perpendicular drawn from the point (1,0,3) on a line passing though $(α, 7, 1)$ is $(\frac{5}{3}, \frac{7}{3}, \frac{17}{3})$ , then $α$ is equal to ______

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Solution

Since PQ is perpendicular to L, therefore
$(1 - \frac{5}{3}) (α - \frac{5}{3}) + (\frac{- 7}{3}) (7 - \frac{7}{3}) + (3 - \frac{17}{3}) (1 - \frac{17}{3}) = 0$
$\Rightarrow \frac{- 2 α}{3} + \frac{10}{9} - \frac{98}{9} + \frac{112}{9} = 0$
$\Rightarrow \frac{2 α}{3} = \frac{24}{9} \Rightarrow α = 4$

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Straight lines in 3D

Remember concepts with our Masterclasses.

If the foot of the perpendicular drawn from the point (1,0,3) on a line passing though α,7,1 is53,73,173, then α is equal to ______

Since PQ is perpendicular to L, therefore1−53α−53+−737-73+3−1731−173=0⇒−2α3+109−989+1129=0⇒2α3=249⇒α=4

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If the foot of the perpendicular drawn from the point (1,0,3) on a line passing though $(α, 7, 1)$ is $(\frac{5}{3}, \frac{7}{3}, \frac{17}{3})$ , then $α$ is equal to ______