AP EAMCET · Maths · Three Dimensional Geometry
If \((\alpha, \beta, \gamma)\) are the Direction cosines of an angular bisector of two lines whose Direction ratios are \((2,2,1)\) and \((2,-1,-2)\), then \((\alpha+\beta+\gamma)^2=\)
- A \(3\)
- B \(2\)
- C \(4\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
Given, direction ratio are \((2,2,1)\) and \((2,-1,-2)\) Now, angle between the lines is given by \(\cos \theta=\frac{4-2-2}{\sqrt{9} \cdot \sqrt{9}}=0 \Rightarrow \theta=\frac{\pi}{2}\) So, direction cosines of two lines are…
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
- \(\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x=\)AP EAMCET 2024 Medium
- On solving \(\frac{d y}{d x}=\frac{x-y+3}{2 x-2 y+5}\), the solution obtained is \(x=2(x-y)+\log (t)+c\), find \(t\)AP EAMCET 2020 Medium
- Let \(\bar{a}\) and \(\bar{b}\) be two non-collinear unit vectors. If \(\bar{u}=\bar{a}-(\bar{a} \cdot \bar{b}) \bar{b}\) and \(\bar{v}=\bar{a} \times \bar{b}\), then \(|\bar{v}|=\)AP EAMCET 2017 Hard
- In \(\triangle \mathrm{ABC}\), if \(\cos \mathrm{A}+\cos \mathrm{C}=4 \sin ^2 \frac{\mathrm{B}}{2}\), then the ratio between the perimeter of the triangle and \((a+c)\) isAP EAMCET 2023 Hard
- If \(a, b, c, d\) are real numbers such that \(a < b < c < d\), then the roots of the equation \((x-a)(x-c)+2(x-b)(x-d)=0\) areAP EAMCET 2022 Medium
- A circle is such that \((x-2) \cos \theta+(y-2) \sin \theta=1\) touches it for all values of \(\theta\). Then, the circle isAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- The frequency of fifth harmonic of a closed pipe is equal to the frequency of third harmonic of an open pipe. If the length of the open pipe is 72 cm . then the length of the closed pipe isAP EAMCET 2024 Easy
- The de Broglie wavelength associated with an electron accelerated through a potential difference of \(\frac{200}{3} \mathrm{~V}\) is nearlyAP EAMCET 2025 Medium
- A variable line passing through a fixed point \((\alpha, \beta)\) intersects the coordinate axes at \(A\) and \(B\). If \(O\) is the origin, then the locus of the centroid of the \(\triangle O A B\) isAP EAMCET 2018 Medium
- The transformed equation of \(3 x^2-6 x y+8 y^2=8\) when the axes are rotated about the origin through an angle \(\frac{\pi}{4}\) in the positive direction, isAP EAMCET 2018 Medium
- The centre of the circle \(r^2-4 r(\cos \theta+\sin \theta)-4=0\) in cartesian coordinates isAP EAMCET 2004 Medium
- When the origin is shifted to the point \((2,3)\) and then the coordinate axes are rotated through an angle \(\frac{\pi}{3}\) in the counter clockwise sense, then the transformed equation of \(3 x^2+2 x y+3 y^2-18 x-22 y+50=0\) isAP EAMCET 2018 Hard