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 Questions on Vectors
- If \( \mathbf{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}, \mathbf{b} = -\hat{i} + 2\hat{j} + \hat{k} \) and \( \mathbf{c} = 3\hat{i} + \hat{j} \) are the vectors such that \( \mathbf{a} + \lambda \mathbf{b} \) is perpendicular to \( \mathbf{c} \), then the value of \( \lambda \) is:
- If cos(12/13) + sin(P), then the value of P is:
- If the angle between the line \( 2(x + 1) = y = z \) and the plane \( 2x - y + \sqrt{2} z + 4 = 0 \) is \( \frac{\pi}{6} \), then the value of \( \lambda \) is:
- If the volume of the tetrahedron, whose vertices are \( A(1, 2, 3), B(-3, -1, 1), C(2, 1, 3) \) and \( D(-1, 2, x) \), is \( \frac{11}{6} \) cubic units, then the value of \( x \) is:
- Approximate value of \( \cos 59^\circ \) is:
Questions Asked in JEE Main exam
The remainder when \( 64^{64} \) is divided by 7 is equal to:
- JEE Main - 2025
- Arithmetic Progression
- The sum of the infinite series $ \cot^{-1} \left( \frac{7}{4} \right) + \cot^{-1} \left( \frac{19}{4} \right) + \cot^{-1} \left( \frac{39}{4} \right) + \cot^{-1} \left( \frac{67}{4} \right) + ... $ is:
- JEE Main - 2025
- Sequence and series
- If $ \alpha $ is a root of the equation $ x^2 + x + 1 = 0 $ and $$ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20$$, then n is equal to _______
- JEE Main - 2025
- Sequence and series
x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)
- JEE Main - 2025
- Equilibrium
- The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
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