WBJEE · Maths · Three Dimensional Geometry
A line with positive direction cosines passes through the point \(\mathrm{P}(2,-1,2)\) and makes equal angle with co-ordinate axes. The line meets the plane \(2 x+y+z=9\) at point \(Q\). The length of the line segment \(P Q\) equals.
- A 1 unit
- B \(\sqrt{2}\) unit
- C \(\sqrt{3}\) unit
- D 2 unit
Answer & Solution
Correct Answer
(C) \(\sqrt{3}\) unit
Step-by-step Solution
Detailed explanation
Let d.c. of line is \((\mathrm{k}, \mathrm{k}, \mathrm{k})\) \(\begin{array}{l} \Rightarrow 3 \mathrm{k}^{2}=1 \Rightarrow \mathrm{k}=\frac{1}{\sqrt{3}} \\ \Rightarrow \text { d.c. of line is }\left(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right) \end{array}\)…
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
- The equation \(r \cos \theta=2 a \sin ^2 \theta\) represents the curveWBJEE 2024 Easy
- The population \(p(t)\) at time \(t\) of a certain mouse species follows the differential equation \(\frac{d p(t)}{d t}=0.5 p(t)-450\). If \(p(0)=850\), then the time at which the population becomes zero isWBJEE 2025 Medium
- Maximum value of the function \(f(x)=\frac{x}{8}+\frac{2}{x}\) on the interval [1,6] isWBJEE 2012 Medium
- \(\int \frac{\sin ^{-1} x}{\sqrt{1-x^2}} d x\) is equal to
where \(c\) is an arbitrary constantWBJEE 2009 Easy - Let \(\int \frac{x^{1 / 2}}{\sqrt{1-x^3}} d x=\frac{2}{3} g(f(x))+c\); thenWBJEE 2022 Medium
- The least positive value of \(t\), so that the lines \(x=t+\alpha, y+16=0 \quad\) and \(\quad y=\alpha x\) are concurrent, isWBJEE 2015 Medium
More PYQs from WBJEE
- Let \(f\) be a non-constant continuous function for all \(x \geq 0\). Let \(f\) satisfy the relation \(f(x) f(a-x)=1\) for some \(a \in R^{+}\). Then, \(I=\int_{0}^{a} \frac{d x}{1+f(x)}\) is equal toWBJEE 2017 Medium
- In the crystalline solid \(M \mathrm{SO}_{4} \cdot n \mathrm{H}_{2} \mathrm{O}\) of molar mass 250 g \(mol^{-1}\) , the percentage of anhydrous salt is 64 by weight. The value of \(n\) isWBJEE 2019 Medium
- If the matrix \(M_r\) is given by \(M_r=\left(\begin{array}{cc}r & r-1 \\ r-1 & r\end{array}\right)\) for \(r=1,2,3, \ldots\) then \(\operatorname{det}\left(\mathrm{M}_1\right)+\operatorname{det}\left(\mathrm{M}_2\right)+\ldots . .+\operatorname{det}\left(\mathrm{M}_{2008}\right)=\)WBJEE 2023 Medium
- A frictionless piston-cylinder based enclosure contains some amount of gas at a pressure of \(400 \mathrm{kPa}\). Then heat is transferred fo the gas at constant pressure in a quasi-static process. The piston moves up slowly through a height of \(10 \mathrm{cm} .\) If the piston has a cross-sectional area of \(0.3 \mathrm{m}^{2},\) the work done by the gas in this process isWBJEE 2013 Medium
- When \(\mathrm{H}_{2} \mathrm{O}_{2}\) is shaken with an acidified solution of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) in the presence of ether, the cthereal layer turns blue due to the formation ofWBJEE 2012 Medium
- A spherical convex surface of power 5 dioptre separates object and image space of refractive indices \(1.0\) and \(\frac{4}{3}\) respectively. The radius of curvature of the surface isWBJEE 2021 Medium