MHT CET · Maths · Three Dimensional Geometry
The line drawn \((4,-1,2)\) and \((-3,2,3)\) meets the plane at right angles at the point \((-10,5,4)\) then the equation of plane is
- A \(2 x-y-z+29=0\)
- B \(7 x-3 y-z+89=0\)
- C \(x-y+z+11=0\)
- D \(x+y+z+1=0\)
Answer & Solution
Correct Answer
(B) \(7 x-3 y-z+89=0\)
Step-by-step Solution
Detailed explanation
d.r's of normal to the plane are \( < 4-(-3),-1-2\), \(2-3>^0 < 7,-3,-1>\)
and it passes through \((-10,5,4)\). Hence the required equation is
\(\begin{aligned}
& 7(x-(-10))-3(y-5)-1(z-4)=0 \\
& \Rightarrow 7 x-3 y-z+89=0
\end{aligned}\)
and it passes through \((-10,5,4)\). Hence the required equation is
\(\begin{aligned}
& 7(x-(-10))-3(y-5)-1(z-4)=0 \\
& \Rightarrow 7 x-3 y-z+89=0
\end{aligned}\)
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
- \( \int \frac{x^2+1}{x\left(x^2-1\right)} \mathrm{d} x= \)MHT CET 2023 Medium
- Let \(\vec{u}, \vec{v}\) and \(\vec{w}\) be vectors such that \(|\vec{u}+\vec{v}+\vec{w}=\overline{0}|\). If \(|\vec{u}|=3\), \(\overrightarrow{|v|}=4\) and \(\overrightarrow{|w|}=5\), then the value of \(|\vec{u} \cdot \vec{v}+\vec{v} \cdot \vec{w}+\vec{w} \cdot \vec{u}|\) isMHT CET 2022 Easy
- \(\int \frac{x^{2}+1}{x^{4}+x^{2}+1} d x=\)MHT CET 2020 Hard
- Let \(\hat{a}\) and \(\hat{b}\) be two unit vectors. If the vectors \(\bar{c}=\hat{a}+2 \hat{b}\) and \(\bar{d}=5 \hat{a}+4 \hat{b}\) are perpendicular to each other, then the angle between \(\hat{a}\) and \(\hat{b}\) isMHT CET 2024 Medium
- If \(\operatorname{cosec} \theta+\cot \theta=5\), then \(\sin \theta=\)MHT CET 2020 Medium
- If \(y=\left(x^x\right) x\), then \(\frac{d y}{d x}=\)MHT CET 2022 Medium
More PYQs from MHT CET
- If \(x=\mathrm{t}^2+\mathrm{t}+1, \mathrm{y}=\sin \left(\frac{\mathrm{t} \pi}{2}\right)+\cos \left(\frac{\mathrm{t} \pi}{2}\right)\), then \(\frac{\mathrm{dy}}{\mathrm{d} x}\) at \(\mathrm{t}=1\) isMHT CET 2025 Medium
- Five capacitors, each of capacity 'C' are connected as shown in the figure. The resultant capacity between A & B is \(14 \mu \mathrm{~F}\). The capacity of each capacitor is
MHT CET 2025 Medium - Two identical long parallel wires carry currents ' \(\mathrm{I}_1\) ' and ' \(\mathrm{I}_2\) ' such that \(\mathrm{I}_1>\mathrm{I}_2\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(8 \times 10^{-6} \mathrm{~T}\). If the direction of \(\mathrm{I}_2\) is reversed, the field becomes \(3.2 \times 10^{-5} \mathrm{~T}\). The ratio of \(\mathrm{I}_2\) to \(\mathrm{I}_1\) isMHT CET 2025 Medium
- The Cartesian equation of the line passing through the point \((-3,0,1)\) and perpendicular to vectors \(\hat{i}-2 \widehat{j}+\widehat{k}\) and \(2 \hat{i}+\widehat{j}-\widehat{k}\) isMHT CET 2022 Easy
- The solubility of sparingly soluble salt \(\mathrm{AB}_2\) is \(1.0 \times 10^{-4} \mathrm{~mol}\) \(\mathrm{dm}^{-3}\). What is its solubility product?MHT CET 2021 Medium
- Which from following reagents is used in the conversion of phenol to picric acid?MHT CET 2024 Medium