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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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