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Three Dimensional Geometry

Question
CBSEENMA12033452
Wired Faculty App

The planes: 2x – y + 4 z = 5 and 5.x – 2.5 y + 10 z = 6 are

  • Perpendicular

  • Parallel

  • intersect y-axis

  • passes through open parentheses 0 comma space 0 comma space 5 over 4 close parentheses

Solution

B.

Parallel

The equations of given planes are
2x – y + 4z = 5 and 5x –2.5y + 10z = 6
Now,       2 over 5 space equals space fraction numerator negative 1 over denominator negative 2.5 end fraction space equals space 4 over 10
rightwards double arrow space space space space space space space space space space 2 over 5 space equals space fraction numerator 1 over denominator begin display style 25 over 10 end style end fraction space equals 4 over 10 space space space rightwards double arrow space space space space 2 over 5 space equals space 2 over 5 space equals 2 over 5 space space space space space open square brackets because space space straight a subscript 1 over straight a subscript 2 equals straight b subscript 1 over straight b subscript 2 equals straight c subscript 1 over straight c subscript 2 close square brackets
∴ given planes are parallel

Some More Questions From Three Dimensional Geometry Chapter

Find the direction cosines of x, y and z-axis.

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