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Condition for Concurrency of Three Lines

35. Let two l...

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35. Let two lines L1 and L2 be 2x-2y+3z-2=0=x-y+z+1 And x+2y-z-3=0=3x-y+2z-1 Respectively. Find the vector along the normal of the plane containing the two lines.

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Q. Equation of lines

L_{1} : 2 x - 2 y + 3 z - 2 = 0 = x - y + z + 1 = 0

L_{2} : x + 2 y - z - 3 = 0 = 3 x - y + 2 z - 1 = 0

Distance of point

P (0, 0, 0)

from the plane containing

L_{1}

L_{2}

and measured along the line

x = y = z

\frac{a \sqrt{a}}{b}

a

b

are coprime numbers) then

a + b

Q. The equation of the plane containing the two lines of intersection of the two pairs of planes x + 2y – z – 3 = 0 and 3x – y + 2z – 1 = 0, 2x – 2y + 3z = 0 and x – y + z + 1 =0 is :

L_{1}

is the line of intersection of the planes

2 x - 2 y + 3 z - 2 = 0, x - y + z + 1 = 0

L_{2}

is the line of intersection of the planes

x + 2 y - z - 3 = 0, 3 x - y + 2 z - 1 = 0

, then the distance of the origin from the plane, containing the lines

L_{1}

L_{2}

Q. Equation of the plane containing the line

x + 2 y + 3 z - 5 = 0 = 3 x + 2 y + z - 5

which is parallel to the line

x - 1 = 2 - y = z - 3

Q. The equation of the plane passing through the point

(- 1, 2, 0)

and parallel to the lines

L_{1} : \frac{x}{3} = \frac{y + 1}{0} = \frac{z - 2}{- 1}

L_{2} : \frac{x - 1}{1} = \frac{2 y + 1}{2} = \frac{z + 1}{- 1}

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Condition for Concurrency of Three Lines

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