The direction angles of the line x -4 z -3- y -2-3 z are - - and Y- then cos-cos-cos Y -A- 2-26B- -28-26C-D- 2

The correct option is A 2√(26)x=4z+3, y=2 3z ⇒x 34=y 2 3= z1 Hence, direction angles are given by cosα=4√(26),cosβ= 3√(26) and cosγ=1√(26) ⇒cosα+cosβ+cosγ=2√(2 ...

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Standard XII

Mathematics

Perpendicular Distance of a Point from a Plane

The direction...

Question

The direction angles of the line $x = 4 z + 3, y = 2 - 3 z$ are $α, β$ and $γ$ , then $cos α + cos β + cos γ =$ ____

\frac{2}{\sqrt{26}}

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\frac{8}{\sqrt{26}}

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Solution

The correct option is A $\frac{2}{\sqrt{26}}$
$x = 4 z + 3, y = 2 - 3 z$
$\Rightarrow \frac{x - 3}{4} = \frac{y - 2}{- 3} = \frac{z}{1}$
Hence, direction angles are given by
$cos α = \frac{4}{\sqrt{26}}, cos β = \frac{- 3}{\sqrt{26}}$ and $cos γ = \frac{1}{\sqrt{26}}$
$\Rightarrow cos α + cos β + cos γ = \frac{2}{\sqrt{26}}$

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