First slide

Straight lines in 3D

Question

Which of the following is correct to the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$

Moderate

A

It passes through the origin
B

It passes through the point $(2, 1, 5)$
C

it lies on $x y -$ plane
D

It is equally inclined with axes.

Solution

$T h e s y m m e t r i c f o r m o f t h e l i n e p a s \sin g t h r o u g h t h e p o i n t (x_{1}, y_{1}, z_{1}) a n d h a v i n g d i r e c t i o n r a t i o s (l, m, n) i s \frac{x - x_{1}}{l} = \frac{y - y_{1}}{m} = \frac{z - z_{1}}{n}$ $H e n c e, t h e g i v e n l i n e i s p a s \sin g t h r o u g h t h e o r i g i n$

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