Equation of the plane passing through the point 1-2-3 and containg the line r -2- -1-2 - -1-3 - k- isA- 5 x-y-z-10B- 5 x-y-z-6C- x-5 y-3 x-2D- x-5 y-3 z-0

The correct option is A 5x+y+z=10r̅ =(2 + λ) î 1 + 2 λ) ĵ+ (1 3 λ) k̂ =(2i j+k)+λ (i 2j 3k) ⇒ this line is passing through (2, 1,1) and parallel to the line ...

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Byju's Answer

Standard XII

Mathematics

Image of a Point with Respect to a Plane

Equation of t...

Question

Equation of the plane passing through the point (1,2,3) and containg the line $¯ r = (2 + λ)^i - (1 + 2 λ)^j + (1 - 3 λ)^k$ is

5x-y+z=6

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x+5y-3x=2

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x-5y+3z=0

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5x+y+z=10

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Solution

The correct option is D 5x+y+z=10
$¯ r = (2 + λ)^i - 1 + 2 λ)^j + (1 - 3 λ)^k$
$= (2 i - j + k) + λ (i - 2 j - 3 k)$
$\Rightarrow$ this line is passing through (2,-1,1) and parallel to the line with d. $r^{'} s$ (1,-2,-3)
Required plane passing through (1,2,3) $∴$ Equation of plane is
$∣ ∣ ∣ ∣ \begin{matrix} x - 1 & y - 2 & z - 3 1 & - 3 & - 2 1 & - 2 & - 3 \end{matrix} ∣ ∣ ∣ ∣ = 0$
i.e., $5 x + y + z = 10$

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Equation of the plane passing through the point (1,2,3) and containg the line ¯r=(2+λ)^i−(1+2λ)^j+(1−3λ)^k is

Equation of the plane passing through the point (1,2,3) and containg the line $¯ r = (2 + λ)^i - (1 + 2 λ)^j + (1 - 3 λ)^k$ is