If the line- x-3-2-y-2-1-z-4-3 lies in the plane- - x-m y-z-9- then -2-m2 is equal to -A- 18B- 5C- 2D- 26

The correct option is C 2 Line is perpendicular to normal of plane ⇒ (2 î ĵ + 3 k̂) . (l î + m ĵ k̂) = 0 2l – m – 3 = 0 ……. (i) (3, –2, –4) lies on the pla ...

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Byju's Answer

Standard XII

Mathematics

Condition for a Line to Lie on a Plane

If the line, ...

Question

If the line, $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane, $ℓ x + m y - z = 9, t h e n ℓ^{2} + m^{2}$ is equal to :

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Solution

The correct option is C
2

Line is perpendicular to normal of plane

$\Rightarrow (2^i -^j + 3^k) . (l^i + m^j -^k) = 0$

2l – m – 3 = 0 ……. (i)

(3, –2, –4) lies on the plane

3l – 2m + 4 = 9

3l – 2m = 5 ……. (ii)

Solving (i) and (ii)

l = 1, m = –1

$l^{2} + m^{2} = 2$

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Similar questions

If the line, $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane, lx+my-z = 9, then $l^{2} + m^{2}$ is equal to

Q. If the line,

\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}

lies in the plane,

x + m y - z = 9

, then

l^{2} + m^{2}

is equal to

Q. If the line

\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}

lies in the plane

l x + m y - z = 9

, then

l^{2} + m^{2}

is equal to

If the line, $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane, lx+my-z = 9, then $l^{2} + m^{2}$ is equal to

Q. If the line

\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}

lines in the plane.

l x + m y - z = 9

, then

l^{2} + m^{2}

is equal to:

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If the line, x−32=y+2−1=z+43 lies in the plane, ℓx+my−z=9,then ℓ2+m2 is equal to :

The correct option is C 2 Line is perpendicular to normal of plane ⇒(2^i−^j+3^k).(l^i+m^j−^k)=0 2l – m – 3 = 0 ……. (i) (3, –2, –4) lies on the plane 3l – 2m + 4 = 9 3l – 2m = 5 ……. (ii) Solving (i) and (ii) l = 1, m = –1 l2+m2=2

If the line, $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane, $ℓ x + m y - z = 9, t h e n ℓ^{2} + m^{2}$ is equal to :

The correct option is C
2

Line is perpendicular to normal of plane

$\Rightarrow (2^i -^j + 3^k) . (l^i + m^j -^k) = 0$

2l – m – 3 = 0 ……. (i)

(3, –2, –4) lies on the plane

3l – 2m + 4 = 9

3l – 2m = 5 ……. (ii)

Solving (i) and (ii)

l = 1, m = –1

$l^{2} + m^{2} = 2$