Two bodies of mass \(1\) kg and \(3\) kg have position vectors \(\hat i+2\hat j+\hat k\) and \(−3\hat i−2 \hat j+\hat k\), respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector.
\(\hat i+2\hat j+\hat k\)
\(−3\hat i−2 \hat j+\hat k\)
\(−2\hat j+2\hat k\)
\(−2\hat i−\hat j+2\hat k\)
The Correct Option is A
Solution and Explanation
\(\bar r_{com}=\frac {m_1\bar r_1+m_2\bar r_2}{ m_1+m_2}\)
\(\bar r_{com}=\frac {(1−9)\hat i+(2−6)\hat j+(1+3)\hat k}{4}\)
\(\bar r_{com}=\frac {-8\hat i-4\hat j+4\hat k}{4}\)
\(\bar r_{com}=−2\hat i−\hat j+\hat k\)
\(|\bar r|=\sqrt {4+1+1}\)
\(|\bar r|=\sqrt 6\)
\(|\hat i+2\hat j+\hat k|=\sqrt 6\)
So, the correct option is (A): \(\hat i+2\hat j+\hat k\)
Top JEE Main Physics Questions
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______
- JEE Main - 2026
- Physics
- Rotational Motion and Torque
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)
- JEE Main - 2026
- Physics
- Gravitation
- Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is _____ ($S$ is the surface tension of mercury).
- JEE Main - 2026
- Physics
- Properties of Fluids
An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ____
- JEE Main - 2026
- Physics
- The Kinetic Theory of Gases
Under steady state condition the potential difference across the capacitor in the circuit is _____ V.
- JEE Main - 2026
- Physics
- Capacitors in DC Circuits
Top JEE Main Vectors Questions
- If position vector is given as \(\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}\) and if its signs are reversed, then which of the following physical quantity remains unaffected?
If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other, then \[ |\vec{a} + \vec{b}| = \sqrt{2} |\vec{a} - \vec{b}| \quad \text{for } |\vec{a}| = n |\vec{b}|. \] The integer value of $n$ is _____.
A vector has magnitude same as that of A = \(-3\hat{i} + 4\hat{j}\) and is parallel to B = \(4\hat{i} + 3\hat{j}\). The x and y components of this vector in the first quadrant are x and y respectively where:
\(x = \_\_\_\_\).
- Find the number of significant digits in the value 10.05
- If $\vec{P}=3 \hat{i}+\sqrt{3} \hat{j}+2 \hat{k}$ and $\vec{Q}=4 \hat{i}+\sqrt{3} \hat{j}+25 \hat{k}$ then, The unit vector in the direction of $\vec{P} \times \vec{Q}$ is $\frac{1}{x}(\sqrt{3} i+\hat{j}-2 \sqrt{3} \hat{k})$ The value of $x$ is
Top JEE Main Questions
Find the area of the region \[ R = \{(x, y) : xy \le 27,\; 1 \le y \le x^2 \}. \]
- JEE Main - 2026
- Integration and Area Calculation
- Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol\(^{-1}\)) in 0.5 L of water at 300 K. Its osmotic pressure is \( x \) bar. Solution B is made by dissolving 2 g of the same protein in 1 L of water at 300 K. Osmotic pressure of solution B is \( y \) bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is \( z \) bar. \( x \), \( y \), and \( z \) respectively are:
- JEE Main - 2026
- Raoult's Law and Colligative Properties
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______
- JEE Main - 2026
- Rotational Motion and Torque
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)
- JEE Main - 2026
- Gravitation
- Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is _____ ($S$ is the surface tension of mercury).
- JEE Main - 2026
- Properties of Fluids
Concepts Used:
Vectors
The quantities having magnitude as well as direction are known as Vectors or Vector quantities. Vectors are the objects which are found in accumulated form in vector spaces accompanying two types of operations. These operations within the vector space include the addition of two vectors and multiplication of the vector with a scalar quantity. These operations can alter the proportions and order of the vector but the result still remains in the vector space. It is often recognized by symbols such as U ,V, and W
Representation of a Vector :
A line having an arrowhead is known as a directed line. A segment of the directed line has both direction and magnitude. This segment of the directed line is known as a vector. It is represented by a or commonly as AB. In this line segment AB, A is the starting point and B is the terminal point of the line.
Types of Vectors:
Here we will be discussing different types of vectors. There are commonly 10 different types of vectors frequently used in maths. The 10 types of vectors are:
- Zero vector
- Unit Vector
- Position Vector
- Co-initial Vector
- Like and Unlike Vectors
- Coplanar Vector
- Collinear Vector
- Equal Vector
- Displacement Vector
- Negative of a Vector