JEE Mains · Maths · STD 11 - 11. introduction to three dimensional geometry
The square of the distance of the point \((-2, -8, 6)\) from the line \(\dfrac{x-1}{1} = \dfrac{y-1}{2} = \dfrac{z}{-1}\) along the line \(\dfrac{x+5}{1} = \dfrac{y+5}{-1} = \dfrac{z}{2}\) is equal to:
- A \(3\)
- B \(6\)
- C \(8\)
- D \(12\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Let the given point be \(P(-2, -8, 6)\). The distance is measured along the line \(\dfrac{x+5}{1} = \dfrac{y+5}{-1} = \dfrac{z}{2}\), which has direction ratios \((1, -1, 2)\). The equation of the line passing through \(P\) and parallel to this line 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 \(\cos \,\left( {\alpha + \beta } \right) = \frac{3}{5},\,\sin \,\left( {\alpha - \beta } \right) = \frac{5}{{13}}\) and \(0 < \alpha ,\beta < \frac{\pi }{4}\) then \(\tan \,\left( {2\alpha } \right)\) is equal toJEE Mains 2019 Hard
- Let \(y=y(x)\) be the solution of the differential equation \(d y=e^{a x+y} d x ; \alpha \in N\). If \(y\left(\log _{e} 2\right)=\log _{e} 2\) and \(y(0)=\log _{e}\left(\frac{1}{2}\right)\), then the value of \(\alpha\) is equal to \(.....\)JEE Mains 2021 Medium
- If \(\lim _{x \rightarrow \infty}\left(\left(\frac{\mathrm{e}}{1-\mathrm{e}}\right)\left(\frac{1}{\mathrm{e}}-\frac{x}{1+x}\right)\right)^x=\alpha\), then the value of \(\frac{\log _{\mathrm{e}} \alpha}{1+\log _{\mathrm{e}} \alpha}\) equals :JEE Mains 2025 Medium
- The number of integral values of \(k\), for which one root of the equation \(2 x^2-8 x+k=0\) lies in the interval \((1,2)\) and its other root lies in the interval \((2,3)\), is :JEE Mains 2023 Hard
- The value of \(\left(\frac{1+\sin \frac{2 \pi}{9}+i \cos \frac{2 \pi}{9}}{1+\sin \frac{2 \pi}{9}-i \cos \frac{2 \pi}{9}}\right)^3\) isJEE Mains 2023 Medium
- If the projection of the vector \(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}}\) on the sum of the two vectors \(2 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}-5 \hat{\mathrm{k}}\) and \(-\lambda \hat{i}+2 \hat{j}+3 \hat{k}\) is \(1,\) then \(\lambda\) is equal to ..... .JEE Mains 2021 Medium
More PYQs from JEE Mains
- If \(\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]\), then the number of solutions of \(\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0\), is equal toJEE Mains 2025 Medium
- If \(\int \limits_0^1 \frac{1}{\left(5+2 x -2 x ^2\right)\left(1+ e ^{(2-4 x)}\right)} dx =\frac{1}{\alpha} \log _{ e }\left(\frac{\alpha+1}{\beta}\right)\) \(\alpha, \beta > 0\), then \(\alpha^4-\beta^4\) is equal to:JEE Mains 2023 Hard
- Consider the quadratic equation \((n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0\), \(n \in \mathbb{R}\). Let \(\alpha\) be the minimum value of the product of its roots and \(\beta\) be the maximum value of the sum of its roots. Then the sum of the first six terms of the G.P., whose first term is \(\alpha\) and the common ratio is \(\dfrac{\alpha}{\beta}\), is :JEE Mains 2026 Hard
- Let integers \(\mathrm{a}, \mathrm{b} \in[-3,3]\) be such that \(\mathrm{a}+\mathrm{b} \neq 0\). Then the number of all possible ordered pairs
(a, b), for which \(\left|\frac{z-\mathrm{a}}{z+\mathrm{b}}\right|=1\) and \(\left|\begin{array}{ccc}z+1 & \omega & \omega^2 \\ \omega & z+\omega^2 & 1 \\ \omega^2 & 1 & z+\omega\end{array}\right|=1, z \in \mathrm{C}\), where \(\omega\) and \(\omega^2\) are the roots of \(x^2+x+1=0\), is equal to ________.JEE Mains 2025 Hard - Let \(\vec{a_k} = (\tan\theta_k)\hat{i} + \hat{j}\) and \(\vec{b_k} = \hat{i} - (\cot\theta_k)\hat{j}\), where \(\theta_k = \dfrac{2^{k-1}\pi}{2^n + 1}\), for some \(n \in \mathbb{N}\), \(n > 5\). Then the value of \(\dfrac{\displaystyle\sum_{k=1}^{n}|\vec{a_k}|^2}{\displaystyle\sum_{k=1}^{n}|\vec{b_k}|^2}\) is _____.JEE Mains 2026 Hard
- Given below two statements:
Statement I: \(25^{13}+20^{13}+8^{13}+3^{13}\) is divisible by 7.
Statement II: The integral part of \((7+4\sqrt{3})^{25}\) is an odd number.
In the light of the above statements, choose the correct answer from the options given belowJEE Mains 2026 Hard