Question:medium

A vector \(\sqrt{3}\hat{i} + \hat{j}\) rotates about its tail through an angle 30\(^\circ\) in clock wise direction then the new vector is

Show Hint

Always check the magnitude first. The magnitude must remain 2. Options (c) and (d) have magnitudes 1 and can be eliminated immediately.

Updated On: Apr 19, 2026

Show Solution

Solution and Explanation

Was this answer helpful?

0

Top Questions on Vectors

The shortest distance between the lines \[ \vec r=\frac13\hat i+2\hat j+\frac83\hat k+\lambda(2\hat i-5\hat j+6\hat k) \] \[ \vec r=\left(-\frac23\hat i-\frac13\hat k\right)+\mu(\hat j-\hat k), \quad \lambda,\mu\in\mathbb R \] is
- JEE Main - 2026
- Mathematics
- Vectors
View Solution
If \(\hat u,\hat v\) are unit vectors and \[ |\hat u\times \hat v|=\frac{\sqrt3}{2} \] and \[ \vec A=\lambda\hat u+\hat v+\hat u\times \hat v \] then find \(\lambda\). (Angle between \(\hat u\) and \(\hat v\) is acute)
- JEE Main - 2026
- Mathematics
- Vectors
View Solution
Let \( A = \begin{bmatrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \end{bmatrix} \). If \( B = [b_{ij}]_{3 \times 3} \) and \( B = A^{99} - I \), then find \( \frac{b_{31} - b_{21}}{b_{32}} \).
- JEE Main - 2026
- Mathematics
- Vectors
View Solution
If system of equations \(x \cos \theta - 8y - 12z = 0\), \(x \cos 2\theta + y + 3z = 0\), \(x + y + 3z = 0\) has non-trivial solution, then find sum of values of \(\theta\) (where \(\theta \in [0, 2\pi]\)).
- JEE Main - 2026
- Mathematics
- Vectors
View Solution
Want to practice more? Try solving extra ecology questions todayView All Questions

Questions Asked in BITSAT exam

A passenger sitting in a train A moving at 90 km/h observes another train B moving in the opposite direction for 8 s. If the velocity of the train B is 54 km/h, then length of train B is:

BITSAT - 2026
Relative Velocity

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

BITSAT - 2026
Definite Integral

If \( x = \sqrt{2^{\text{cosec}^{-1} t}} \) and \( y = \sqrt{2^{\text{sec}^{-1} t}} (|t| \ge 1) \), then dy/dx is equal to :

BITSAT - 2026
Derivatives of Functions in Parametric Forms

The Bohr orbit radius for the hydrogen atom (n = 1) is approximately 0.530 \AA. The radius for the first excited state (n = 2) orbit is (in \AA)

BITSAT - 2026
Bohr's model of hydrogen atom