MHT CET · Maths · Three Dimensional Geometry
The equation of a plane containing the point \((1,-1,1)\) and parallel to the plane
\(2 x+3 y-4 z=17\) is
- A \(\bar{r}_{\cdot}(2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k})=-5\)
- B \(\bar{r} \cdot(2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k})=-15\)
- C \(\bar{r} \cdot(4 \hat{\imath}+3 \hat{\jmath}-4 \hat{k})=-3\)
- D \(\bar{r} \cdot(3 \hat{\imath}+4 \hat{\jmath}-2 \hat{k})=-3\)
Answer & Solution
Correct Answer
(A) \(\bar{r}_{\cdot}(2 \hat{\imath}+3 \hat{\jmath}-4 \hat{k})=-5\)
Step-by-step Solution
Detailed explanation
Equation of plane passing through the point having position vector \(\bar{a}\) and normal to \(\overline{\mathrm{n}}\) is
\(\therefore \overline{\mathrm{r}} \cdot \overline{\mathrm{n}} \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})=(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}) \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}~-\) \(4 \hat{\mathrm{k}})=2-3-4=-5\)
\(\therefore \overline{\mathrm{r}} \cdot \overline{\mathrm{n}} \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})=(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}}) \cdot(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}~-\) \(4 \hat{\mathrm{k}})=2-3-4=-5\)
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 \(\overline{\mathrm{a}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overline{\mathrm{b}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-\hat{\mathrm{k}}\) are two vectors, then the angle between the vectors \(3 \bar{a}+5 \bar{b}\) and \(5 \bar{a}+3 \bar{b}\) isMHT CET 2024 Easy
- \(\lim _{x \rightarrow 1} \frac{a b^x-a^x b}{x^2-1}=\)MHT CET 2021 Medium
- Rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant and it is found that the number doubles in 6 hours. The number of bacteria becomes times at the end of 18 hours.MHT CET 2023 Medium
- The equation of the plane through the intersection of the planes \(\mathrm{x}+\mathrm{y}+\mathrm{z}=1\) and \(2 \mathrm{x}+3 \mathrm{y}-\mathrm{x}+4=0\) and parallel to \(\mathrm{X}\)-axis isMHT CET 2022 Medium
- Derivative of with respect to isMHT CET 2019 Medium
- \(\int \frac{\log \left(x+\sqrt{1+x^2}\right)}{\sqrt{1+x^2}} \mathrm{~d} x=\frac{1}{2}(g(x))^2+C\), (where \(C\) is constant of integration.) Then \(g(x)=\)MHT CET 2022 Medium
More PYQs from MHT CET
- Which of the following is effectively used to remove E. coli bacteria from water?MHT CET 2025 Easy
- Select the correct match from the following:MHT CET 2024 Easy
- \(If \frac{x}{x-y}=\log \left(\frac{a}{x-y}\right), \text { then } \frac{d y}{d x}=\)MHT CET 2020 Easy
- The material used for solar cell should have band gapMHT CET 2025 Easy
- What is the volume of 1 mole of a crystalline solid having unit cell edge length \(16 \times 10^{-8} \mathrm{~cm}\), if it's unit cell contains 24 molecules?MHT CET 2020 Medium
- Identify the element having highest ionization enthalpy.MHT CET 2023 Easy