The distance between the plane r -5 -k-5and the line r -2 -2 -3 k-4 k- isA- 10-3-3B- 10-2 -3C- 10-3 -310D- 3

The correct option is C 103√(3)Observe that (i+5j+k).(i j+4k)=0 ⇒ Line is ∥ to the plane ∴ required distance = distance from (2, 2,3) to the plane x+5y+z=5 is ...

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Byju's Answer

Standard XII

Mathematics

Equation of a Plane : General Form

The distance ...

Question

The distance between the plane $\to r . (^i + 5^j +^k) = 5$
and the line $\to r = 2^i - 2^j + 3^k + λ (^i -^j + 4^k)$ is

\frac{10}{\sqrt{3}}

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\frac{10}{2 \sqrt{3}}

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\frac{10}{3 \sqrt{3}}

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\frac{10}{3}

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Solution

The correct option is C $\frac{10}{3 \sqrt{3}}$
Observe that $(i + 5 j + k) . (i - j + 4 k) = 0$
$\Rightarrow$ Line is $∥$ to the plane
$∴$ required distance $=$ distance from $(2, - 2, 3)$ to the plane $x + 5 y + z = 5$ is
$= \frac{| 2 - 10 + 3 - 5 |}{\sqrt{1 + 25 + 1}} = \frac{10}{3 \sqrt{3}}$

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The distance between the plane →r.(^i+5^j+^k)=5 and the line →r=2^i−2^j+3^k+λ(^i−^j+4^k) is

The correct option is C 103√3Observe that (i+5j+k).(i−j+4k)=0 ⇒ Line is ∥ to the plane ∴ required distance = distance from (2,−2,3) to the plane x+5y+z=5 is =|2−10+3−5|√1+25+1=103√3

The distance between the plane $\to r . (^i + 5^j +^k) = 5$
and the line $\to r = 2^i - 2^j + 3^k + λ (^i -^j + 4^k)$ is