TS EAMCET · Maths · Three Dimensional Geometry
The direction cosines of the line passing through \(P(2,3-1)\) and the origin are
- A \(\frac{2}{\sqrt{14}}, \frac{3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- B \(\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- C \(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
- D \(\frac{2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{-1}{\sqrt{14}}\)
Answer & Solution
Correct Answer
(C) \(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\)
Step-by-step Solution
Detailed explanation
The direction cosines of \(O P\) \(\begin{aligned} & =\left(\frac{-2}{\sqrt{4+9+1}}, \frac{-3}{\sqrt{4+9+1}}, \frac{1}{\sqrt{4+9+1}}\right) \\ & =\left(\frac{-2}{\sqrt{14}}, \frac{-3}{\sqrt{14}}, \frac{1}{\sqrt{14}}\right) \end{aligned}\)
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
- Let \(\mathrm{A}, \mathrm{B}\) be two \(3 \times 3\) matrices and \(\mathrm{C}\) be a \(3 \times 3\) unit matrix such that \(A B-C\) is a non-singular matrix. Let \(\mathrm{D}=(\mathrm{AB}-\mathrm{C})^{-1}\). Then, consider the following statements.
Statement I : \(\operatorname{det}(\mathrm{BA})=\operatorname{det}(\mathrm{BA}-\mathrm{C}) \operatorname{det}(\mathrm{BDA})\)
Statement II : ABD = DAB
Which of the above statements is (are) true?TS EAMCET 2022 Medium - If the solution \(y(x)\) of the differential equation \(\sin x \frac{d y}{d x}+y \cos x=e^{2 x}, x \in(0, \pi)\) satisfies \(y\left(\frac{\pi}{2}\right)=0\), then \(y\left(\frac{\pi}{6}\right)=\)TS EAMCET 2020 Hard
- The perimeter of a sector is a constant. If its area is to be maximum, the sectorial angle is :TS EAMCET 2006 Medium
- If is the normal form of the equation of a straight line and are respectively intercepts of this line, thenTS EAMCET 2019 Easy
- \((1,-2,1)\) is a point on a plane \(\pi\) and \(\pi\) is parallel to the plane \(x-y-z=0\). If the equation of \(\pi\) is \(a x+b y+c z-2\) \(=0\), then \(b-2 c=\)TS EAMCET 2023 Easy
- The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things isTS EAMCET 2024 Medium
More PYQs from TS EAMCET
- \(\int \frac{x^3}{\sqrt{1+x^2}} d x\) is equal toTS EAMCET 2016 Easy
- Which one of the following compounds is having maximum 'lone pair-lone pair' electron repulsions?TS EAMCET 2023 Medium
- Which of the following statement(s) are correct, when alkali metals burn in the presence of oxygen? I. Lithium forms monoxide II. Sodium forms peroxide III. Potassium, rubidium and cesium forms superoxideTS EAMCET 2020 Easy
- A cylindrical vessel of height \(50 \mathrm{~cm}\) is filled with water and rests on a table. A small hole is made at the height \(h\) from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance \(x_{\max }\) from the vessel as shown in the figure. The value of \(x_{\max }\) will be (Neglect the viscosity of water.)
TS EAMCET 2019 Hard - The correct order of " \(\Delta_f \mathrm{H}^{\circ}\) " values of Diamond (I), Graphite (II) and Fullerene (III) isTS EAMCET 2022 Easy
- The normal at a point on the parabola \(y^2=4 x\) passes through \((5,0)\). If there are two more normals to this parabola which pass through \((5,0)\), the centroid of the triangle formed by the feet of these three normals isTS EAMCET 2020 Medium