$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise sense. If,with respect to the new system,$\vec{a}$ has components $p+1$ and $1$,then:
- A$p=0$
- B$p=-1$ or $p=\frac{1}{3}$
- C$p=1$ or $p=-\frac{1}{3}$
- D$p=1$ or $p=-1$
Explore More
Similar Questions
If $\vec{p} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{q} = \hat{i} + \hat{j} - \hat{k}$,and $\vec{a}$ and $\vec{b}$ are two vectors such that $\vec{p} = 2\vec{a} + \vec{b}$ and $\vec{q} = \vec{a} + 2\vec{b}$,then the angle between $\vec{a}$ and $\vec{b}$ is:
Difficult
View SolutionIf non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$,find the angle between $\vec{a}$ and $\vec{c}$.
Medium
View SolutionIf $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $\overrightarrow{a}_1=2 \hat{i}-\hat{j}+\hat{k}$,$\overrightarrow{a}_2=3 \hat{i}-4 \hat{j}-4 \hat{k}$,$\overrightarrow{a}_3=\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{a}_4=-\hat{i}+3 \hat{j}+\hat{k}$,then the correct order of $m_1, m_2, m_3$ and $m_4$ is
DifficultAP EAMCET 2009
View SolutionGiven $\overrightarrow{p} = 3 \hat{i} + 2 \hat{j} + 4 \hat{k}$,$\overrightarrow{a} = \hat{i} + \hat{j}$,$\overrightarrow{b} = \hat{j} + \hat{k}$,$\overrightarrow{c} = \hat{i} + \hat{k}$ and $\overrightarrow{p} = x \overrightarrow{a} + y \overrightarrow{b} + z \overrightarrow{c}$,then $x, y, z$ are respectively:
The direction cosines of the vector $\vec{a} = -2 \hat{i} + \hat{j} - 5 \hat{k}$ are
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo