If the line, lies in the plane, ℓx + my – z = 9, then ℓ2 + m2 is equal to

Engineering

Mathematics

Plane and Its Different Forms

Question

If the line, $\frac{x - 3}{2} = \frac{y + 2}{- 1} = \frac{z + 4}{3}$ lies in the plane, ℓx + my – z = 9, then ℓ² + m² is equal to

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

P : ℓx + my – z = 9, the

point (3, – 2, – 4) lies on the plane

3ℓ – 2m + 4 = 9

⇒ 3ℓ – 2m = 5 ….…(1)

$\bar{n} \cdot \bar{b}$ = 2ℓ – m – 3 = 0 ….…(2)

Solving (1) & (2), ℓ = 1 and m = – 1

$∴$ ℓ² + m² = 2.