JEE Mains · Physics · STD 11 - 3.1 vectors
In the cube of side \(a\) shown in the figure, the vector from the central point of the face \(ABOD\) to the central point of the face \(BEFO\) will be
- A \(\frac{1}{2}\,a\,\left( {\hat k - \hat i} \right)\)
- B \(\frac{1}{2}\,a\,\left( {\hat i - \hat k} \right)\)
- C \(\frac{1}{2}\,a\,\left( {\hat j - \hat i} \right)\)
- D \(\frac{1}{2}\,a\,\left( {\hat j - \hat k} \right)\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\,a\,\left( {\hat j - \hat i} \right)\)
Step-by-step Solution
Detailed explanation
Position vector of \(G\) is \(\overrightarrow{O G}=\frac{a \vec{i}}{2}+\frac{a}{2} \vec{k}\) Position vector of \(H\) is \(\overrightarrow{O H}=\frac{a}{2} \vec{j}+\frac{a}{2} \vec{k}\) \(\overrightarrow{G H}=\frac{a}{2}(\vec{j}-\vec{i})\)
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
- A planar loop made of wire is rotating in a uniform magnetic field. At time \(t=0\), the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of \(10\) seconds, at which of the following times will the induced electromotive force (emf) be maximum and minimum, respectively?JEE Mains 2020 Hard
- Eight equal drops of water are falling through air with a steady speed of \(10\,cm / s\). If the drops coalesce, the new velocity is \(.........\,cm/s\)JEE Mains 2023 Hard
- From the top of a tower, a ball is thrown vertically upward which reaches the ground in \(6 \,s\). A second ball thrown vertically downward from the same position with the same speed reaches the ground in \(1.5\, s\). A third ball released, from the rest from the same location, will reach the ground in........ \(s\).JEE Mains 2022 Hard
- A solid conducting sphere, having a charge \(Q\), is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be \(V\). If the shell is now given a charge of \(-4\, Q\), the new potential difference between the same two surface is......\(V\)JEE Mains 2019 Hard
- A uniform cable of mass \(‘M’\) and length \(‘L’\) is placed on a horizontal surface such that its \({\left( {\frac{1}{n}} \right)^{th}}\) part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should beJEE Mains 2019 Hard
- A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from \(440\, Hz\) to \(480 \,Hz ,\) when it gets reflected from the wall. If the speed of sound in air is \(345 \,m / s ,\) then the speed of the car is \(.......km/hr\)JEE Mains 2020 Medium
More PYQs from JEE Mains
- Which of the following expressions corresponds to simple harmonic motion along a straight line, where \(x\) is the displacement and \(a, b, c\) are positive constants?JEE Mains 2014 Medium
- The value closest to the thermal velocity of a Helium atom at room temperature \((300\,K)\)in \(ms^{-1}\) is \([k_B\, = 1 .4\times10^{-23}\,J/K;\, m_{He}\, = 7\times10^{-27}\,kg]\)JEE Mains 2018 Medium
- Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) Diffusion current in a \(p-n\) junction is greater than the drift current in magnitude if the junction is forward biased. Reason \(R:\) Diffusion current in a \(p-n\) junction is from the \(n\)-side to the \(p\)-side if the junction is forward biased. In the light of the above statements, choose the most appropriate answer from the options given belowJEE Mains 2023 Medium
- In an ac circuit, an inductor, a capacitor and a resistor are connected in series with \({X}_{{L}}={R}={X}_{{C}}\). Impedance of this circuit is:JEE Mains 2021 Easy
- A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W , is operated at 15 V . The approximate value of protective resistance in this circuit is _________ \(\Omega\).JEE Mains 2026 Easy
- A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is \(\frac{2 \mathrm{~A}}{3}\). The new amplitude of motion is \(\frac{\mathrm{nA}}{3}\). The value of \(\mathrm{n}\) is____.JEE Mains 2024 Hard