JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \(P\) be the foot of the perpendicular from the point \(Q(10,-3,-1)\) on the line \(\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z+1}{-2}\). Then the area of the right angled triangle \(P Q R\), where \(R\) is the point \((3,-2,1)\), is
- A \(9 \sqrt{15}\)
- B \(\sqrt{30}\)
- C \(8 \sqrt{15}\)
- D \(3 \sqrt{30}\)
Answer & Solution
Correct Answer
(D) \(3 \sqrt{30}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \frac{\mathrm{x}-3}{7}=\frac{\mathrm{y}-2}{-1}=\frac{\mathrm{z}+1}{-2}=\lambda \\ & \Rightarrow 7 \lambda+3,-\lambda+2,-2 \lambda-1 \\ & \text {dr's of QP } \Rightarrow 7 \lambda-7,-\lambda+5,-2 \lambda \end{aligned}\) Now…
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 \(L\) be a line obtained from the intersection of two planes \(x+2 y+z=6\) and \(y+2 z=4\) If point \(P (\alpha, \beta, \gamma)\) is the foot of perpendicular from \((3,2,1)\) on \(L ,\) then the value of \(21(\alpha+\beta+\gamma)\) equals ...... .JEE Mains 2021 Hard
- Two lines \(\frac{{x - 3}}{1} = \frac{{y + 1}}{3} = \frac{{z - 6}}{{ - 1}}\) and \(\frac{{x + 5}}{7} = \frac{{y - 2}}{{ - 6}} = \frac{{z - 3}}{4}\) intersect at the point \(R\). The reflection of \(R\) in the \(xy -\) plane has coordinatesJEE Mains 2019 Hard
- If \(\lim _{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{m \sqrt{5}}{n(2 n)^{2 / 3}}\), where \(\operatorname{gcd}(m, n)=1\), then \(8 m+12 n\) is equal to ...........JEE Mains 2024 Hard
- Let the shortest distance from \((\mathrm{a}, 0), \mathrm{a}\gt0\), to the parabola \(y^2=4 x\) be 4 . Then the equation of the circle passing through the point \((a, 0)\) and the focus of the parabola, and having its centre on the axis of the parabola is :JEE Mains 2025 Medium
- Consider three boxes, each containing \(10\) balls labelled \(1, 2, ….., 10\). Suppose one ball is randomly drawn from each of the boxes. Denote by \(n_i\), the label of the ball drawn from the \(i^{th}\) box, \((i = 1, 2, 3)\). Then, the number of ways in which the balls can be chosen such that \(n_1 < n_2 < n_3\) is:JEE Mains 2019 Hard
- Let \(\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}\) be a function which satisfies \(\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y}) \forall \mathrm{x}, \mathrm{y} \in \mathrm{R} .\) If \(\mathrm{f}(1)=2\) and \(g(n)=\sum \limits_{k=1}^{(n-1)} f(k), n \in N\) then the value of \(n,\) for which \(\mathrm{g}(\mathrm{n})=20,\) isJEE Mains 2020 Hard
More PYQs from JEE Mains
- The number of solutions of the equation \(2 \theta-\cos ^{2} \theta+\sqrt{2}=0\) is \(R\) is equal toJEE Mains 2022 Hard
- The number of elements in the set \(\left\{ n \in N : 10 \leq n \leq 100\right.\) and \(3^{ n }-3\) is a multiple of \(7\}\) is \(........\).JEE Mains 2023 Medium
- If \(z_{1}, z_{2}\) are complex numbers such that \(\operatorname{Re}\left(z_{1}\right)=\left|z_{1}-1\right|, \operatorname{Re}\left(z_{2}\right)=\left|z_{2}-1\right|\) and \(\arg \left(z_{1}-z_{2}\right)=\frac{\pi}{6},\) then \(\operatorname{Im}\left(z_{1}+z_{2}\right)\) is equal toJEE Mains 2020 Hard
- If the lines \(x\,=\,ay\,+\,b,\,\,z\,=\,cy\,+\,d\) and \(x\, = \,a\,'z + \,b\,',\,\,y = \,c\,'z\, + \,d\,'\) are perpendicular, thenJEE Mains 2019 Easy
- If the function \(f(x)=2 x^3-9 a x^2+12 a^2 x+1, a>0\) has a local maximum at \(\mathrm{x}=\alpha\) and a local minimum \(x=\alpha^2\), then \(\alpha\) and \(\alpha^2\) are the roots of the equation :JEE Mains 2024 Hard
- From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :JEE Mains 2025 Hard