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Direction Cosines

The d.rs of t...

Question

The d.rs of the lines $x = a y + b$ , $z = c y + d$ are:

1, a, c

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a, 1, c

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b, 1, c

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c, a, 1

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Solution

The correct option is B $a, 1, c$
Given $x = a y + b$ and $z = c y + d$
$\Rightarrow \frac{x - b}{a} = y$ and $\frac{z - d}{c} = y$
$\Rightarrow \frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}$
Therefore Drs of given line is $a, 1, c$

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Similar questions

Direction ratios of the line represented by the equation x = ay + b, z = cy + d are

x = a y + b, z = c y + d

x = a^{'} z + b^{'}, y = c^{'} z + d^{'}

x = a y + b, z = c y + d, x = a^{'} y + b^{'}, z = c^{'} y + d^{'}

a a^{'} + c c^{'}

x = a y + b, z = c y + d

\frac{x - b}{a} = \frac{y}{1} = \frac{z - d}{c}

a (y + z) = x, b (z + x) = y

c (y + z) = x,

a \neq - 1,

b \neq - 1,

c \neq - 1,

{(1 + a)}^{- 1} + {(1 + b)}^{- 1} + {(1 + c)}^{- 1}

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