JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(ABC\) be a triangle whose circumcentre is at \(P\).If the position vectors \(A, B, C\) and \(P\) are \(\vec a,\vec b,\vec c\) and \(\frac{{\vec a + \vec b + \vec c}}{4}\) respectivey, then the position vector of the orthocentre of this triangle, is
- A \( - \left( {\frac{{\vec a + \vec b + \vec c}}{2}} \right)\)
- B \(\vec a + \vec b + \vec c\)
- C \( \left( {\frac{{\vec a + \vec b + \vec c}}{2}} \right)\)
- D \(\vec 0\)
Answer & Solution
Correct Answer
(C) \( \left( {\frac{{\vec a + \vec b + \vec c}}{2}} \right)\)
Step-by-step Solution
Detailed explanation
Position vector of centriod \(\vec{G}=\begin{array}{c}{\vec{a}+\vec{b}+\vec{c}} \\ {3}\end{array}\) Position vector of circum centre \(\overrightarrow C = \begin{array}{*{20}{c}} {\vec a + \vec b + \vec c}\\ 4 \end{array}\)…
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
- The mean and standard deviation of \(10\) observations are \(20\) and \(84\) respectively. Later on, it was observed that one observation was recorded as \(50\) instead of \(40\). Then the correct variance is:JEE Mains 2023 Hard
- The area bounded by the curve \(4 y^{2}=x^{2}(4-x)(x-2)\) is equal to ...... .JEE Mains 2021 Hard
- If the area of the triangle formed by the positive \(x-\)axis, the normal and the tangent to the circle \((x-2)^{2}+(y-3)^{2}=25\) at the point \((5,7)\) is \(A\) then \(24 A\) is equal to ...... .JEE Mains 2021 Hard
- If \(x^{2}+9 y^{2}-4 x+3=0, x, y \in R\), then \(x\) and \(y\) respectively lie in the intervals:JEE Mains 2021 Hard
- If \(19^{th}\) terms of non -zero \(A.P.\) is zero, then its (\(49^{th}\) term) : (\(29^{th}\) term) isJEE Mains 2019 Hard
- The range of the function \(f ( x )=\sqrt{3-x}+\sqrt{2+x}\) isJEE Mains 2023 Hard
More PYQs from JEE Mains
- If the function \(f\) defined as \(f(x)\, = \frac{1}{x} - \frac{{k - 1}}{{{e^{2x}} - 1}}\) ,\(x\, \ne \,0,\) is continuous at \(x = 0.\) then the ordered pair \((k,f(0))\) is equal to?JEE Mains 2018 Hard
- A complex number z is said to be unimodular if \(\left| z \right| = 1\) . Suppose \(z_1\) and \(z_2\) are complex number such that \(\frac{{{z_1} - 2{z_2}}}{{2 - {z_1}\overline {{z_2}} }}\) is unimodular and \(z_2\) is not unimodular . Then the point \(z_1\) lies on a:JEE Mains 2015 Hard
- Let the length of the focal chord \(P Q\) of the parabola \(y^2=12 x\) be \(15\) units. If the distance of \(P Q\) from the origin is \(\mathrm{p}\), then \(10 \mathrm{p}^2\) is equal to ...........JEE Mains 2024 Hard
- The region represented by \(\{z=x+i y \in C:|z|-\operatorname{Re}(z) \leq 1\}\) is also given by the inequalityJEE Mains 2020 Hard
- The smallest positive integral value of \( a \), for which all the roots of \( x^{4}-ax^{2}+9=0 \) are real and distinct, is equal toJEE Mains 2026 Hard
- \(\int \limits_{-\pi}^{\pi}|\pi-| x || d x\) is equal to :JEE Mains 2020 Medium