The length of the perpendicular from the point (2,

Engineering

Mathematics

Equation of Straight Line in 3D and Distance Of a Point From Line

Question

The length of the perpendicular from the point (2, –1, 4) on the straight line, $\frac{x + 3}{10} = \frac{y - 2}{- 7} = \frac{z}{1}$ is

greater than 2 but less than 3

greater than 4

less than 2

greater than 3 but less than 4

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$Now, \vec{MP} . (10 \hat{i} - i \hat{j} + \hat{k}) = 0$

$\Rightarrow λ = \frac{1}{2}$

$∴$ Length of perpendicular

$(= PM) = \sqrt{0 + \frac{1}{4} + \frac{49}{4}}$

$= \sqrt{\frac{50}{4}} = \sqrt{\frac{25}{4}} = \frac{5}{\sqrt{2}}$

Which is greater then 3 but less than 4.