MHT CET · Maths · Three Dimensional Geometry
The length of the foot of the perpendicular from the point \(\left(1, \frac{3}{2}, 2\right)\) to the plane \(2 x-2 y+4 z+17=0\) is
- A \(\sqrt{6}\) units
- B \(3 \sqrt{3}\) units
- C \(4 \sqrt{3}\) units
- D \(2 \sqrt{6}\) units
Answer & Solution
Correct Answer
(D) \(2 \sqrt{6}\) units
Step-by-step Solution
Detailed explanation
\(d = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}}\) \(d = \frac{|2(1) - 2\left(\frac{3}{2}\right) + 4(2) + 17|}{\sqrt{2^2 + (-2)^2 + 4^2}}\)
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
- An open tank with a square bottom, to contain 4000 cubic cm . of liquid, is to be constructed. The dimensions of the tank, so that the surface area of the tank is minimum, areMHT CET 2024 Medium
- A unit vector coplanar with \(\hat{i}+\hat{j}+\hat{k}\) and \(2 \hat{i}+\hat{j}+\hat{k}\) and perpendicular to \(\hat{i}+\hat{j}-\hat{k}\) isMHT CET 2024 Medium
- Let \(P(3,2,6)\) be a point in space and \(Q\) be a point on the line \(\vec{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(-3 \hat{i}+\hat{j}+5 \hat{k})\). Then the value of \(\mu\) for which the vector \(P \vec{Q}\) is parallel to the plane \(x-4 y+3 z=1\) is:MHT CET 2024 Medium
- \(\int_{-5}^{5}\left[\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}\right] d x=\)MHT CET 2020 Easy
- A vector with magnitude of 3 units, which is perpendicular to each of the vectors \(\bar{a}=3 \hat{i}+\hat{j}-4 \hat{k}\) and \(\bar{b}=6 \hat{i}+5 \hat{j}-2 \hat{k}\), is given byMHT CET 2022 Easy
- If the area bounded by the curve \(x^2=4 \mathrm{y}\), X-axis and the line \(x=4\) is divided into equal areas by the line \(x=\alpha\), then the value of \(\alpha\) is ...MHT CET 2025 Medium
More PYQs from MHT CET
- If thenMHT CET 2017 Medium
- An electron of mass ' \(m_e\) ' and a proton of mass ' \(m_p\) ' are kept in a uniform electric field. The ratio of the acceleration of electron \(\left(a_e\right)\) to the acceleration of proton \(\left(a_p\right)\) isMHT CET 2022 Easy
- The instantaneous values of current and voltage in an AC circuit are given by \(I=6 \sin \left(100 \pi t+\frac{\pi}{4}\right)\) and \(V=5 \sin \left(100 \pi t-\frac{\pi}{4}\right)\), thenMHT CET 2022 Easy
- For every value of \(x \in[1,3]\), the function \(f(x)=\frac{1}{8^x}\) isMHT CET 2022 Easy
- The rate constant of a first order reaction is \(1.15 \times 10^{-3} \mathrm{~s}^{-1}\). How long will 5 g of reactant take to reduce to 3 g ?MHT CET 2025 Medium
- Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and radius of the first wire is twice the radius of the second wire then the ratio of the lengths of the first wire to second wire isMHT CET 2017 Medium