AP EAMCET · Maths · Three Dimensional Geometry
\(P, Q, R\) and \(S\) are four points with the position vectors \(3 \mathbf{i}-4 \mathbf{j}+5 \mathbf{k},-4 \mathbf{i}+5 \mathbf{j}+\mathbf{k}\) and \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\), respectively. Then, the line \(P Q\) meets the line \(R S\) at the point
- A \(3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\)
- B \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\)
- C \(-\mathbf{i}+4 \mathbf{j}+\mathbf{k}\)
- D \(\mathbf{i}+\mathbf{j}+\mathbf{k}\)
Answer & Solution
Correct Answer
(B) \(-3 \mathbf{i}+4 \mathbf{j}+3 \mathbf{k}\)
Step-by-step Solution
Detailed explanation
Let the coordinates of four points \(P, Q, R\) and \(S\) be \((3,-4,5), \quad(0,0,4), \quad(-4,5,1) \quad\) and \(\quad(-3,4,3)\) respectively. Now, equation of line \(P Q\) is…
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
- If \(\Delta(x)=\left|\begin{array}{cc}e^x & -1 \\ \sin x-1 & 1\end{array}\right|\), then \(\lim _{x \rightarrow 0} \frac{\Delta(x)}{x}=\)AP EAMCET 2017 Easy
- Let \(1, \omega\) and \(\omega^2\) be the cube roots of unity. What is the value of \(\left(1-\omega+\omega^{-1}\right)^5-2\left(1+\omega-\omega^{-1}\right)^4=\) ?AP EAMCET 2021 Easy
- If the system of equations \(2 x+p y+6 z=8, x+2 y+q z=5\) and \(x+y+3 z=4\) has infinitely many solutions, then \(\mathrm{p}=\)AP EAMCET 2025 Medium
- After the coordinate axes are rotated through an angle \(\frac{\pi}{4}\) in the anti clockwise direction without shifting the origin, if the equation \(x^2+y^2-2 x-4 y-20=0\) transforms to \(a x^2+2 h x y+b y^2+2 g x+2 f y+c=0\) in the new coordinate system, then \(\left|\begin{array}{lll}a & h & g \\ h & b & f \\ g & f & c\end{array}\right|=\)AP EAMCET 2025 Hard
- If \(f(x)=x^5-5 x^4+5 x^3-10\) has its local maxima and minima at \(x=a\) and \(x=b\) respectively, then \(2 a+b\) is equal toAP EAMCET 2021 Medium
- The area of the triangle formed by the tangent to the curve \(x y=\mathrm{a}^2\) at \(\left(x_1, y_1\right)\) on it and the axes isAP EAMCET 2022 Medium
More PYQs from AP EAMCET
- When a body is in , then match the following.
Velocity is maximum Acceleration is maximum is of total energy At mean position is of total energy At half of the amplitude Acceleration is maximum At times the amplitude AP EAMCET 2019 Easy - If \(\alpha\) and \(\beta(\alpha>\beta)\) are the multiple roots of the equation \(4 x^4+4 x^3-23 x^2-12 x\) \(+36=0\), then \(2 \alpha-\beta=\)AP EAMCET 2025 Medium
- \(\mathrm{SF}_6\) is a kinetically inert substance becauseAP EAMCET 2020 Medium
- Three numbers are chosen from 1 to 30. The probability that they are not three consecutive numbers isAP EAMCET 2025 Medium
- The correct order of adsorption of the following gases on the surface of charcoal is
\(\begin{array}{llllll}\mathrm{H}_2 & \mathrm{CH}_4 & \mathrm{SO}_2 & \mathrm{H}_2 & \mathrm{CH}_4 & \mathrm{SO}_2 \\ \mathbf{I} & \mathbf{I I} & \text { III } & \mathbf{I} & \text { II } & \text { III }\end{array}\)AP EAMCET 2022 Easy - A proton and an \(\alpha\)-particle are simultaneously projected in opposite direction into a region of uniform magnetic field of \(2 \mathrm{mT}\) perpendicular to the direction of the field. After some time it is found that the velocity of proton has changed in direction by \(90^{\circ}\). Then at this time, the angle between the velocity vectors of proton and \(\alpha\)-particle isAP EAMCET 2019 Hard