Let a plane P contain two linesr- - - andr-k- - -If Q- - - is the foot of the perpendicular drawn from the point M1-0-1 to P- then 3- equals

N=î amp;ĵ amp;k̂ 1 amp;1 amp;0 0 amp;1 amp; 1 n= î+ĵ+k̂ Equation of plane P is nbsp; ⇒ 1(x 1)+1(y 0)+1(z 0)=0 ⇒ x y z 1=0 If Q(α,β,γ) is t ...

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Perpendicular Distance of a Point from a Line

Let a plane P...

Question

Let a plane $P$ contain two lines
$\to r =^i + λ (^i +^j), λ \in R$ and
$\to r = -^j + μ (^j -^k), μ \in R .$
If $Q (α, β, γ)$ is the foot of the perpendicular drawn from the point $M (1, 0, 1)$ to $P$ , then $3 (α + β + γ)$ equals

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L

\to r \cdot (^i -^j + 2^k) = 2

\to r \cdot (2^i +^j -^k) = 2

P (α, β, γ)

L

(1, 2, 0)

35 (α + β + γ)

(2, 1, 4)

\to r = (^i +^j) + λ (^i + 2^j -^k)

\to r = (^i +^j) + μ (-^i +^j - 2^k)

α^i +^j +^k,^i + β^j +^k,^i +^j + λ^k (α, β, γ \neq 1)

\frac{1}{1 - α} + \frac{1}{1 + β} + \frac{1}{1 - γ}

α, β, γ

[tan α^i +^j +^k,^i + tan β^j +^k,^i +^j + tan γ^k]

\to α = a^i + b^j + c^k, \to β = b^i + c^j + a^k

\to γ = c^i + a^j + b^k

\to α \neq \to β \neq \to γ

\to r =^i +^j +^k,

\to r

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