JEE Mains · Physics · STD 11 - 3.1 vectors
Two vectors \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) have equal magnitude. The magnitude of \((\overrightarrow{{X}}-\overrightarrow{{Y}})\) is \({n}\) times the magnitude of \((\overrightarrow{{X}}+\overrightarrow{{Y}})\). The angle between \(\overrightarrow{{X}}\) and \(\overrightarrow{{Y}}\) is -
- A \(\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)\)
- B \(\cos ^{-1}\left(\frac{{n}^{2}-1}{-{n}^{2}-1}\right)\)
- C \(\cos ^{-1}\left(\frac{-n^{2}-1}{n^{2}-1}\right)\)
- D \(\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)\)
Answer & Solution
Correct Answer
(B) \(\cos ^{-1}\left(\frac{{n}^{2}-1}{-{n}^{2}-1}\right)\)
Step-by-step Solution
Detailed explanation
Given \(X=Y\) \(\sqrt{ X ^{2}+ Y ^{2}-2 \times Y \cos \theta}\) \(= n \sqrt{ X ^{2}+ Y ^{2}+2 \times Y \cos \theta}\) Square both sides \(2 X ^{2}(1-\cos \theta)= n ^{2} \cdot 2 X ^{2}(1+\cos \theta)\) \(1-\cos \theta= n ^{2}+ n ^{2} \cos \theta\)…
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 Physics
- Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is
JEE Mains 2022 Medium - A mass of \(50\, {kg}\) is placed at the centre of a uniform spherical shell of mass \(100\, {kg}\) and radius \(50 \,{m}\). If the gravitational potential at a point, \(25\, {m}\) from the centre is \({V} \,{kg} / {m} .\) The value of \({V}\) isJEE Mains 2021 Medium
- Given below are two statements: Statement \(I:\) Rotation of the earth shows effect on the value of acceleration due to gravity \((g)\). Statement \(II:\) The effect of rotation of the earth on the value of \(g\) at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below.JEE Mains 2023 Medium
- Two coaxial discs, having moments of inertia \(I_1\) and \(\frac{I_1}{2}\) are a rotating with respectively angular velocities \(\omega_1\) and \(\frac{\omega_1}{2}\), about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If \(E_f\) and \(E_i\) are the final and initial total energies, then \((E_f -E_i)\) isJEE Mains 2019 Hard
- A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a \(400 \Omega\) resistor connected in series, the zener current is found to be 4 times load current. The load current \(\left(I_L\right)\) and load resistance \(\left(R_{\mathrm{L}}\right)\) are :JEE Mains 2025 Easy
- A plane electromagnetic wave of wavelength \(\lambda \) has an intensity \(I.\) It is propagating along the positive \(Y-\) direction. The allowed expressions for the electric and magnetic fields are given byJEE Mains 2018 Medium
More PYQs from JEE Mains
- Let \(\eta_{1}\) is the efficiency of an engine at \(T _{1}=447^{\circ}\,C\) and \(T _{2}=147^{\circ}\,C\) while \(\eta_{2}\) is the efficiency at \(T _{1}=947^{\circ}\,C\) and \(T _{2}=47^{\circ}\,C\). The ratio \(\frac{\eta_{1}}{\eta_{2}}\) will be.JEE Mains 2022 Medium
- A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).)JEE Mains 2013 Hard
- An object of mass 8 kg is hanging from one end of a uniform rod \(C D\) of mass 2 kg and length 1 m pivoted at its end \(C\) on a vertical wall as shown in figure. It is supported by a cable \(A B\) such that the system is in equilibrium. The tension in the cable is:
(Take \(g=10 m s ^{-2}\) )
JEE Mains 2023 Medium - The acute angle between the pair of tangents drawn to the ellipse \(2 x^{2}+3 y^{2}=5\) from the point \((1,3)\) is.JEE Mains 2022 Hard
- Let \(\alpha=8-14 i , A=\left\{ z \in C : \frac{\alpha z -\bar{\alpha} \overline{ z }}{ z ^2-(\overline{ z })^2-112 i }=1\right\}\) and \(B =\{ z \in C :| z +3 i |=4\}\) Then \(\sum_{z \in A \cap B}(\operatorname{Re} z-\operatorname{Im} z)\) is equal to \(...............\).JEE Mains 2023 Hard
- Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " \(q\) " is released at a distance " \(a\) " from the wire with a speed \(v_0\) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \(x\) from the wire. The value of \(x\) is [ \(\mu_0\) is vacuum permeability]JEE Mains 2025 Hard