JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let \((\alpha, \beta, \gamma)\) be the foot of perpendicular from the point \((1,2,3)\) on the line \(\frac{x+3}{5}=\frac{y-1}{2}=\frac{z+4}{3}\). then \(19(\alpha+\beta+\gamma)\) is equal to :
- A \(102\)
- B \(101\)
- C \(99\)
- D \(100\)
Answer & Solution
Correct Answer
(B) \(101\)
Step-by-step Solution
Detailed explanation
Let foot \(P(5 k-3,2 k+1,3 k-4)\) DR's \(\rightarrow\) AP: \(5 \mathrm{k}-4,2 \mathrm{k}-1,3 \mathrm{k}-7\) DR's \(\rightarrow\) Line: \(5,2,3\) Condition of perpendicular lines \((25 k-20)+(4 k-2)+(9 k-21)=0\) Then \(\mathrm{k}=\frac{43}{38}\) Then…
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 \(P = \left\{ {\theta :\sin \,\theta - \cos \,\theta = \sqrt 2 \,\cos \,\theta } \right\}\) and \(Q = \left\{ {\theta :\sin \,\theta + \cos \,\theta = \sqrt {2\,} \sin \,\theta } \right\}\) be two sets. ThenJEE Mains 2016 Hard
- If the function \(f\,:\,R - \,\{ 1, - 1\} \to A\) defined by \(f\,(x)\, = \frac{{{x^2}}}{{1 - {x^2}}},\) is surjective, then \(A\) is equal toJEE Mains 2019 Hard
- For each \(t \in R\) ,let \(\left[ t \right]\) be the greatest interger less than or equal to \(t\) . Then \(\mathop {\lim }\limits_{x \to 0 + } x\left( {\left[ {\frac{1}{x}} \right] + \left[ {\frac{2}{x}} \right] + .\;.\;.\; + \left[ {\frac{{15}}{x}} \right]} \right) =\) . .. . .JEE Mains 2018 Hard
- Consider a triangle \(\mathrm{ABC}\) having the vertices \(\mathrm{A}(1,2), \mathrm{B}(\alpha, \beta)\) and \(\mathrm{C}(\gamma, \delta)\) and angles \(\angle \mathrm{ABC}=\frac{\pi}{6}\) and \(\angle \mathrm{BAC}=\frac{2 \pi}{3}\). If the points \(\mathrm{B}\) and \(\mathrm{C}\) lie on the line \(\mathrm{y}=\mathrm{x}+4\), then \(\alpha^2+\gamma^2\) is equal to ....................JEE Mains 2024 Hard
- If the line, \(2 x-y+3=0\) is at a distance \(\frac{1}{\sqrt{5}}\) and \(\frac{2}{\sqrt{5}}\) from the lines \(4 x-2 y+\alpha=0\) and \(6 x-3 y+\beta=0,\) respectively, then the sum of all possible values of \(\alpha\) and \(\beta\) isJEE Mains 2020 Medium
- The sum of the absolute maximum and absolute minimum values of the function \(f(x)=\tan ^{-1}(\sin x-\cos x)\) in the interval \([0, \pi]\) is.JEE Mains 2022 Hard
More PYQs from JEE Mains
- Let \(A=\left[\begin{array}{lll}0 & 1 & 2 \\ a & 0 & 3 \\ 1 & c & 0\end{array}\right]\), where \(a, c \in R\). If \(A^3=A\) and the positive value of a belongs to the interval ( \(n -1, n\) ], where \(n \in N\), then \(n\) is equal to \(..........\).JEE Mains 2023 Hard
- If the distance between the plane, \(23 \mathrm{x}-10 \mathrm{y}-2 \mathrm{z}+48=0\) and the plane containing the lines \(\frac{x+1}{2}=\frac{y-3}{4}=\frac{z+1}{3}\) and \(\frac{x+3}{2}=\frac{y+2}{6}=\frac{z-1}{\lambda}(\lambda \in R)\) is equal to \(\frac{\mathrm{k}}{\sqrt{633}},\) then \(\mathrm{k}\) is equal toJEE Mains 2020 Hard
- Let \(a, b, c\) and \(d\) be non-zero numbers. If the point of intersection of the lines \(4ax + 2ay + c = 0\) and \(5bx + 2by + d =0\) lies in the fourth quadrant and is equidistant from the two axes thenJEE Mains 2014 Hard
- For \(p\,>\,0\), a vector \(\vec{v}_{2}=2 \hat{i}+(p+1) \hat{j}\) is obtained by rotating the vector \(\vec{v}_{1}=\sqrt{3} p \hat{i}+\hat{j}\) by an angle \(\theta\) about origin in counter clockwise direction. If \(\tan \theta=\frac{(\alpha \sqrt{3}-2)}{4 \sqrt{3}+3}\), then the value of \(\alpha\) is equal to \(....\)JEE Mains 2021 Hard
- The value of \(lim_{x\rightarrow0}\frac{log_{e}(sec(ex) \cdot sec(e^{2}x)\cdot...\cdot sec(e^{10}x))}{e^{2}-e^{2cos~x}}\) is equal toJEE Mains 2026 Hard
- Let a function \(f:\left( {0,\infty } \right) \to \left( {0,\infty } \right)\) be defined by \(f\left( x \right) = \left| {1 - \frac{1}{x}} \right|\). Then \(f\) isJEE Mains 2019 Hard