If the distance of the point P(4, 3, 5) from the Y-axis is λ, then the value of 7λ2 is.

Engineering

Mathematics

Direction Cosines and Direction Ratio

theorem in space

Distance from a Plane

Question

If the distance of the point P(4, 3, 5) from the Y-axis is λ, then the value of 7λ² is.

$7 \sqrt{41}$

287

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⇒ A = (x₁,y₁,z₁) = (0,3,0) and P = (x₂,y₂,z₂) = (4,3,5)

Here, PA = λ

\Rightarrow AP (λ) = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2}}

= \sqrt{(4 - 0)^{2} + (3 - 3)^{2} + (5 - 0)^{2}}

= \sqrt{16 + 0 + 25}

= \sqrt{41}

\Rightarrow 7 λ^{2} = 7 (\sqrt{41})^{2}

= 7 × 41

= 287