Maths · Direction ratios and direction cosines and the angle between two intersecting lines
The planes and are
The planes \( 2 x-y+4 z=5 \) and \( 5 x- \) \( 2.5 y+10 z=6 \) are
- A. Parallel
- B. Perpendicular
- C. Intersect
- D. intersect \( x \) axis
Step-by-step solution
The normal vectors of the planes are (2, -1, 4) and (5, -2.5, 10). Since (5, -2.5, 10) = 2.5 × (2, -1, 4), the normals are parallel. The planes are distinct because the equations are not multiples (2x - y + 4z = 5 vs. 2x - y + 4z = 2.4 after scaling). Hence, the planes are parallel.
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