TS EAMCET · Maths · Three Dimensional Geometry
If \(1,2,3\) and \(-1,0,1\) are the direction ratios of the rays \(\mathbf{O A}\) and \(\mathbf{O B}\) respectively, then the direction cosines of a normal to the plane \(A O B\) are
- A \(\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{-1}{\sqrt{3}}\)
- B \(\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}\)
- C \(\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}\)
- D \(\frac{-3}{13}, \frac{4}{13}, \frac{12}{13}\)
Answer & Solution
Correct Answer
(C) \(\frac{-1}{\sqrt{6}}, \frac{2}{\sqrt{6}}, \frac{-1}{\sqrt{6}}\)
Step-by-step Solution
Detailed explanation
DR's of a normal to the plan \(A O B\) are \[ \left|\begin{array}{rrr} \hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 1 & 2 & 3 \\ -1 & 0 & 1 \end{array}\right|=\langle 2-0,-(1+3), 0+2> \]…
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
- The equation of a curve \(C\) is transformed to \(X^2+Y^2-6 X+8 Y+21=0\) by the rotation of coordinate axes about the origin through an angle of \(\frac{\pi}{4}\) in the positive direction of \(X\)-axis. If \(a x^2+b y^2+c x+d y+e=0\) is the equation of the curve \(C\) before the transformation, then \(\left(a+b+c^2+d^2-5 e\right)^2=0\).TS EAMCET 2021 Hard
- The equation of tangent to the curve \(\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\right)^n=2\) at the point \((a, b)\) isTS EAMCET 2017 Medium
- \(f(x)\) is a twrice differentiable function such that \(f^{\prime \prime}(x)=-f(x)\) and \(f^{\prime}(x)=g(x)\). If \(\left.h(x)=(f(x))^2+g(x)\right)^2\) and \(h(l)=2\), then \(h(2)=\)TS EAMCET 2019 Easy
- The equation of a circle concentric with the circle \(x^2+y^2-6 x+12 y+15=0\) and having area that is twice the area of the given circle isTS EAMCET 2019 Easy
- If \((2-i)\) is one of the roots of the equation \(x^4-9 x^3+31 x^2-49 x+30=0\) and \(\alpha, \beta(\alpha < \beta)\) are its real roots then \(2 \alpha-\beta=\)TS EAMCET 2022 Medium
- \(\left\{x \in R: \frac{14 x}{x+1}-\frac{9 x-30}{x-4} < 0\right\}\) is equal toTS EAMCET 2010 Easy
More PYQs from TS EAMCET
- The difference between the fundamental frequencies of an open pipe and a closed pipe of same length is 100 Hz . The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe isTS EAMCET 2024 Easy
- Let the angle between the lines \(x-2 y+3=0\) and \(k x-y+2=0\) be \(45^{\circ}\). If \(k_1, k_2\left(k_1>k_2\right)\) are two distinct real values of \(k\), then \(k_1-2=\)TS EAMCET 2023 Easy
- If solution of is isotonic with urea solution, the degree of ionisation of is (Molar masses of urea and are and , respectively.)TS EAMCET 2019 Hard
- A black coloured element with \(\mathrm{ns}^2 \mathrm{np}^1\) outer electronic configuration cannot react with air in its crystalline form. However, in amorphous form, it gives an oxide in air which is acidic in nature. Identify the element.TS EAMCET 2022 Medium
- A wooden block of outer volume 1 litre and specific gravity \(\frac{3}{4}\) having a cavity floats with half of its volume immersed in water. Then the volume of the cavity isTS EAMCET 2025 Medium
- The radius of a circular plate is increasing at the rate of \(0.01 \mathrm{~cm} / \mathrm{s}\) when the radius is \(12 \mathrm{~cm}\). Then, the rate at which the area increases, isTS EAMCET 2005 Hard