First slide

Straight lines in 3D

Question

If the lines $x = a z + b$ , $y = c z + d$ ; $x = a_{1} z + b_{1}$ , $y = c_{1} z + d_{1}$ are perpendicular then

Moderate

A

$a a_{1} + c c_{1} + 1 = 0$
B

$a a_{1} + c c_{1} - 1 = 0$
C

$a a_{1} + b b_{1} + 1 = 0$
D

$a a_{1} + d d_{1} - 1 = 0$

Solution

$\frac{x - b}{a} = \frac{y - d}{c} = \frac{z}{1}$ , $\frac{x - b_{1}}{a_{1}} = \frac{y - d_{1}}{c_{1}} = \frac{z}{1}$ both are perpendicular

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