If the equation of a line and a plane be x-3-2-y-4-3-z-5-2 and 4 x-2 y-z-1 respectively-

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Byju's Answer

Standard XII

Mathematics

Equation of Line: Symmetrical Form

If the equati...

Question

If the equation of a line and a plane be $\frac{x + 3}{2} = \frac{y - 4}{3} = \frac{z + 5}{2}$ and 4x-2y-z=1 respectively,

Line is parallel to the plane

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Line is perpendicular to the plane

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Line lies in the plane

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None of these

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Solution

The correct option is A
Line is parallel to the plane

4(2) - 2(3) - 1(2) = 0
Therefore, Line is parallel to the plane.

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Similar questions

Q. Equation of the line passing through the point

(2, 3, 1)

and parallel to the line of the intersection of the plane

x - 2 y - z + 5 = 0 and x + y + 3 z = 6

Q. The equation of the line passing through

(- 4, 3, 1)

, parallel to the plane

x + 2 y - z - 5 = 0

and intersecting the line

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

is:

Q. The equation of the plane containing the straight line

\frac{x}{2} = \frac{y}{3} = \frac{z}{4}

and perpendicular to the plane containing the straight lines

\frac{x}{3} = \frac{y}{4} = \frac{z}{2} and \frac{x}{4} = \frac{y}{2} = \frac{z}{3}

is :

Equation of the plane containing the straight line $\frac{x}{2} = \frac{y}{3} = \frac{z}{4}$ and perpendicular to the plane containing the staight lines $\frac{x}{3} = \frac{y}{4} = \frac{z}{2}$ and $\frac{x}{4} = \frac{y}{2} = \frac{z}{3}$ is

Q. The equation of plane containing intersecting lines

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

and

\frac{x - 3}{4} = \frac{y - 2}{2} = \frac{z - 6}{3}

is _______

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If the equation of a line and a plane be x+32=y−43=z+52 and 4x-2y-z=1 respectively,

The correct option is A Line is parallel to the plane4(2) - 2(3) - 1(2) = 0 Therefore, Line is parallel to the plane.

If the equation of a line and a plane be $\frac{x + 3}{2} = \frac{y - 4}{3} = \frac{z + 5}{2}$ and 4x-2y-z=1 respectively,

The correct option is A
Line is parallel to the plane

4(2) - 2(3) - 1(2) = 0
Therefore, Line is parallel to the plane.