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The planes 2x-y+4z = 5 and 5x-2.5y+10z = 6 -

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Question

The planes `2x - y + 4z` = 5 and `5x - 2.5y + 10z` = 6

Options

  • Perpendicular

  • Parallel

  • Intersect y-axis

  • Paves through `(0, 0, 5/4)`

MCQ

Solution

Parallel

Explanation:

The planes `2x - y + 4z` = 5  ......(i)

`5x - 25y + 10z` = 6  ......(ii)

Comparing the welficents of x, y and z

`2/5 = (-1)/(-25) = 4/10`  ......(iii)

The planes `a_1x + b_1y + c_1z = d_1` and `a_2x + b_2y + c_2z = d_1` are parallel `a_1/a_2 = b_1/b_2 = c_1/c_2`

From (3) this condition is dates fied

As a result, planes (1) and (2) are parallel.

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