AP EAMCET · Maths · Vector Algebra
Let \(A, B\) and \(C\) is three points on a circle of radius \(R\), if \(O\) is the centre of the circle and \(\angle A O B=45^{\circ}, \angle B O C=45^{\circ}\), then the resultant of \(\mathbf{O A}, \mathbf{O B}\) and \(\mathbf{O C}\) has magnitude
- A \(2 R\)
- B \((\sqrt{2}+1) R\)
- C \(2 \sqrt{2} R\)
- D \(4 \sqrt{2} R\)
Answer & Solution
Correct Answer
(B) \((\sqrt{2}+1) R\)
Step-by-step Solution
Detailed explanation
Given, diagram can be projected on \(x y-\) plane as shown here. \(|\mathbf{O A}|=R=|\mathbf{O B}|=|\mathbf{O C}|\) \(\mathbf{O B}\) has projected as \(\mathbf{A} \mathbf{B}^{\prime}\) and \(\mathbf{O C}\) is projected as \(\mathbf{B}^{\prime} \mathbf{C}^{\prime}\). Hence,…
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
- A line \(l\) meets the circle \(x^2+y^2=61\) in \(A, B\) and \(P(-5,6)\) is such that \(P A=P B=10\). Then, the equation of \(l\) isAP EAMCET 2004 Easy
- The equation of the circle passing through the points of intersection of the circles \(x^2+y^2+4 x+6 y-12=0\) and \(x^2+y^2-6 x-4 y-12=0\) and cutting the circle \(x^2+y^2-4 x+4 y+8=0\) orthogonally isAP EAMCET 2018 Medium
- Let \(\mathrm{X}\) - axis be the transverse axis and \(\mathrm{Y}\) - axis be the conjugate axis of a hyperbola \(\mathrm{H}\). Let the eccentricity of \(\mathrm{H}\) be the reciprocal of the eccentricity of the ellipse \(\frac{x^2}{4}+\frac{y^2}{2}=1\). If \((5,4)\) is a point on \(H\), then the length of the transverse axis of \(\mathrm{H}\) isAP EAMCET 2023 Medium
- The locus of a variable point whose chord of contact w.r.t. the hyperbola subtends a right angle at the origin isAP EAMCET 2022 Medium
- The equation of the common tangent to the parabolas \(y^2=32 x\) and \(x^2=256 y\) isAP EAMCET 2017 Medium
- If \((2,-1,3)\) is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane isAP EAMCET 2004 Easy
More PYQs from AP EAMCET
- \(\begin{aligned}
& \text { If }\left[1-\cos \left(\frac{\pi}{2}+\alpha\right)+\sin \left(\frac{3 \pi}{2}+\alpha\right)\right]^2+ \\
& {\left[1-\sin \left(\frac{3 \pi}{2}-\alpha\right)-\cos \left(\frac{3 \pi}{2}+\alpha\right)\right]^2=a+b \sin ^2\left(\frac{\pi}{4}+\alpha\right)}
\end{aligned}\)
then \(a^2+b^2=\)AP EAMCET 2023 Medium - \(\int_{-2}^3\left|1-x^2\right| d x=\)AP EAMCET 2017 Medium
- Photoelectrons are emitted with maximum velocity \(\mathrm{v}\) when light of frequency \(3 \mathrm{f}\) incidents on a photosensitive material of work function \(2 \mathrm{hf}\). If the frequency of the incident light is \(4.25 \mathrm{f}\), the maximum velocity of the emitted photoelectrons is
(h-Plank's constant)AP EAMCET 2023 Medium - \(\frac{d}{d x} \frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x}=f(x)\left[\begin{array}{c}\frac{2}{x+1}+\frac{1}{2(x-1)} \\ -\frac{3}{x+4}-1\end{array}\right]\)then \(f(5)=\)AP EAMCET 2022 Easy
- If a function \(f\) is differentiable on \(\mathbb{R}\) such that \(f^{\prime}(x) \leq 4\) for all \(x \in \mathbb{R}\); and if \(f(2)=-6\) and \(f(6)=8\), then the value of \(f(4)\) belongs to the intervalAP EAMCET 2018 Medium
- The equation of the plane passing through \((1,1,1)\) and \((1,-1,-1)\) and perpendicular to \(2 x-y+z+5=0\) is :AP EAMCET 2003 Medium