TS EAMCET · Maths · Three Dimensional Geometry
If \((\alpha, \beta, \gamma)\) is the foot of the perpendicular drawn from a point \((-1,2,-1)\) to the line joining the points \((2,-1,1)\) and \((1,1,-2)\), then \(\alpha+\beta+\gamma=\)
- A \(2\)
- B \(-\frac{1}{7}\)
- C \(0\)
- D \(\frac{3}{14}\)
Answer & Solution
Correct Answer
(B) \(-\frac{1}{7}\)
Step-by-step Solution
Detailed explanation
Line direction vector: \( \vec{d} = (1-2, 1-(-1), -2-1) = (-1, 2, -3) \) Foot of perpendicular \( (\alpha, \beta, \gamma) = (2-t, -1+2t, 1-3t) \) Vector from point \( (-1,2,-1) \) to foot: \( \vec{P_0F} = (2-t - (-1), -1+2t - 2, 1-3t - (-1)) = (3-t, -3+2t, 2-3t) \) For…
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 be three real numbers. If the function
is continuous everywhere, thenTS EAMCET 2021 Easy - The normal at a point on the parabola \(y^2=4 x\) passes through a point P. Two more normals to this parabola also pass through P. If the centroid of the triangle formed by the feet of these three normals is \(\mathrm{G}(2,0)\), then the abscissa of P isTS EAMCET 2025 Hard
- If \(\Delta_1=\left|\begin{array}{lll}1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3\end{array}\right|\) and \(\Delta_2=\left|\begin{array}{lll}b c & b+c & 1 \\ c a & c+a & 1 \\ a b & a+b & 1\end{array}\right|\), then \(\frac{\Delta_1}{\Delta_2}=\)TS EAMCET 2018 Medium
- The differential equation of a family of hyperbolas whose axes are parallel to coordinate axes, centres lie on the line \(y=2 x\) and eccentricity is \(\sqrt{3}\) isTS EAMCET 2025 Hard
- Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(a x^2+b x+c=0\). Observe the lists given below
The correct match of List-I from List-II is (i) (ii) (iii) (iv)TS EAMCET 2008 Medium - A normal chord PQ drawn at a point P on the parabola \(y^2=5 x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord isTS EAMCET 2025 Medium
More PYQs from TS EAMCET
- Which of the following is/are "not correct" for mixture solution? a) b) Does not obey Raoult's law c) d) An example of ideal solutionTS EAMCET 2022 Medium
- A person fails 4 times in a game when he plays 9 times. If he plays 15 times, the probability of having success at most one isTS EAMCET 2018 Easy
- If \(a x^2-x y-3 y^2-5 x+20 y+c=0\) represents a pair of lines passing through the point \((2,3)\), then \(\mathrm{a}-\mathrm{c}=\)TS EAMCET 2023 Medium
- Three point charges \(1 \mathrm{C},-2 \mathrm{C}\) and \(-2 \mathrm{C}\) are placed at the vertices of an equilateral triangle of side 1 metre. The work done by an external force to increase the separation of the charges to 2 metre in joule is ( \(\varepsilon_0=\) permittivity of air)TS EAMCET 2004 Easy
- \[ \begin{aligned} & \left.\sin ^2 \beta^{\circ}\right)+\sin ^2\left(6^{\circ}\right)+\sin ^2\left(9^{\circ}\right)+\ldots+\sin ^2\left(84^{\circ}\right) \ & +\sin ^2\left(87^{\circ}\right)+\sin ^2\left(90^{\circ}\right)= \end{aligned} \]TS EAMCET 2019 Easy
- If \(1^{\circ}=0.0175\) radians, then the approximate value of \(\sec 58^{\circ}\) isTS EAMCET 2025 Medium