Show that the Following Planes Are at Right Angles. (Ii) X − 2y + 4z = 10 and 18x + 17y + 4z = 49 - Mathematics

Question

Show that the following planes are at right angles.

x − 2y + 4z = 10 and 18x + 17y + 4z = 49

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Solution

$We know that the planes a_{1} x + b_{1} y + c_{1} z + d_{1} = 0 and a_{2} x + b_{2} y + c_{2} z + d_{2} = 0 are perperndicular to each other only if$

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0 .$

$The given planes are x - 2 y + 4 z = 10 and 18 x + 17 y + 4 z = 49 .$

$\Rightarrow a_{1} = 1; b_{1} = - 2; c_{1} = 4; a_{2} = 18; b_{2} = 17; c_{2} = 4$

$Now,$

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = (1) (18) + (- 2) (17) + (4) (4) = 18 - 34 + 16 = 0$

$So, the given planes are perpendicular .$

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Angle Between Two Planes

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Q 3.2 Q 3.1 Q 4.1

Chapter 29: The Plane - Exercise 29.06 [Page 29]

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Chapter 29 The Plane
Exercise 29.06 | Q 3.2 | Page 29

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Show that the Following Planes Are at Right Angles. (Ii) X − 2y + 4z = 10 and 18x + 17y + 4z = 49 - Mathematics

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