CUET · MATHS · PYQ PAPER 2023
The planes 2x - y + 4z = 5 and \(5 x-\frac{5}{2} y+10 z=6\) are
- A perpendicular
- B intersecting at an angle \(\frac{\pi}{4}\)
- C parallel
- D passing through \(\left(0,0, \frac{5}{2}\right)\)
Answer & Solution
Correct Answer
(C) parallel
Step-by-step Solution
Detailed explanation
\(\vec{n_1} = \langle 2, -1, 4 \rangle\) \(\vec{n_2} = \langle 5, -\frac{5}{2}, 10 \rangle\) \(\vec{n_2} = \frac{5}{2} \langle 2, -1, 4 \rangle = \frac{5}{2} \vec{n_1}\) The normal vectors are parallel, so the planes are parallel.
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