MHT CET · Maths · Three Dimensional Geometry
A plane passes through \((2,1,2)\) and \((1,2,1)\) and parallel to the line \(2 x=3 y\) and \(\mathrm{z}=1\), then the plane also passes through the point.
- A \((-6,2,0)\)
- B \((6,-2,0)\)
- C \((-2,0,1)\)
- D \((2,0,1)\)
Answer & Solution
Correct Answer
(C) \((-2,0,1)\)
Step-by-step Solution
Detailed explanation
\(\vec{P_1P_2} = (1-2, 2-1, 1-2) = (-1, 1, -1)\) Line direction vector: \(2x=3y \implies \frac{x}{3}=\frac{y}{2}\). With \(z=1\), \(\vec{d} = (3,2,0)\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(\mathrm{f}(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+\mathrm{m} x}-\sqrt{1-\mathrm{m} x}}{x} & ,-1 \leq x < 0 \ \frac{2 x+1}{x-2} & , 0 \leq x \leq 1\end{array}\right.\) is continuous in the interval \([-1,1]\), then \(\mathrm{m}\) is equal toMHT CET 2023 Easy
- \(\int_5^{10} \frac{d x}{(x-1)(x-2)}=\)MHT CET 2021 Easy
- Let \(\overline{\mathrm{A}}, \overline{\mathrm{B}}, \overline{\mathrm{C}}\) be vectors of lengths 3 units, 4 units, 5 units respectively. let \(\bar{A}\) be perpendicular to \(\overline{\mathrm{B}}+\overline{\mathrm{C}}, \overline{\mathrm{B}}\) be perpendicular to \(\overline{\mathrm{C}}+\overline{\mathrm{A}}\) and \(\overline{\mathrm{C}}\) be perpendicular to \(\overline{\mathrm{A}}+\overline{\mathrm{B}}\), then the length of vector \(\overline{\mathrm{A}}+\overline{\mathrm{B}}+\overline{\mathrm{C}}\) isMHT CET 2024 Easy
- The minimum value for the LPP \(\mathrm{Z}=6 x+2 y\), subject to \(2 x+y \geq 16, x \geq 6, y \geq 1\) isMHT CET 2020 Medium
- The equation of a circle, which passes through the centre of the circle \(x^2+y^2+8 x+10 y-7=0\) and is concentric with the circle. \(2 x^2+2 y^2-8 x-12 y-9=0\), isMHT CET 2022 Easy
- On the interval \([0,1]\) the function \(x^{25}(1-x)^{75}\) takes its maximum value at the pointMHT CET 2007 Medium
More PYQs from MHT CET
- Match the mineral deficiency disorders given in Column I with their symptoms given in Column II.
Choose the correct option from below.Column I Column II i. Chlorosis a. Localised death of tissues in leaves ii. Necrosis b. Premature fall of flowers, fruits and leaves iii. Mottling c. Yellowing of leaves due to absence of chlorophyll iv. Abscission d. Appearance of green and non- green patches on leaves MHT CET 2024 Hard - Which among the following is a Lucas regent?MHT CET 2022 Easy
- The rate of disintegration of a radio active element at time \(\mathrm{t}\) is proportional to its
mass at that time. Then the time during which the original mass of \(1 \cdot 5 \mathrm{gm}\). will
disintegrate into its mass of \(0.5 \mathrm{gm}\). is proportional toMHT CET 2020 Medium - How many methyl groups are present in butylated hydroxytoluene?MHT CET 2020 Medium
- A coil of wire of radius ' \(r\) ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns isMHT CET 2025 Easy
- The unit vector \((a \hat{\imath}+b \hat{j})\) is perpendicular to \((\hat{\imath}+\hat{\jmath})\). The value of \(^{\prime} b^{\prime}\) isMHT CET 2020 Medium