The angle made by the vector $\left( {\hat i\,\, + \;\,\hat j} \right)$ with $x-$ axis and $y$ axis is
The angle made by the vector $\left( {\hat i\,\, + \;\,\hat j} \right)$ with $x-$ axis and $y$ axis is
- A
$45^o, 60^o$
- B
$60^o, 60^o$
- C
$45^o, 45^o$
- D
$60^o, 45^o$
Similar Questions
If $\left| {\vec A } \right|\, = \,2$ and $\left| {\vec B } \right|\, = \,4$ then match the relation in Column $-I$ with the angle $\theta $ between $\vec A$ and $\vec B$ in Column $-II$.
Column $-I$
Column $-II$
$(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$
$(i)$ $\theta = \,{30^o}$
$(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$
$(ii)$ $\theta = \,{45^o}$
$(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$
$(iii)$ $\theta = \,{90^o}$
$(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$
$(iv)$ $\theta = \,{0^o}$
If $\left| {\vec A } \right|\, = \,2$ and $\left| {\vec B } \right|\, = \,4$ then match the relation in Column $-I$ with the angle $\theta $ between $\vec A$ and $\vec B$ in Column $-II$.
| Column $-I$ | Column $-II$ |
| $(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$ | $(i)$ $\theta = \,{30^o}$ |
| $(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$ | $(ii)$ $\theta = \,{45^o}$ |
| $(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$ | $(iii)$ $\theta = \,{90^o}$ |
| $(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$ | $(iv)$ $\theta = \,{0^o}$ |
The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
- [AIPMT 2003]
If two vectors $\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}$ and $\vec{Q}=4 \hat{i}-2 \hat{j}+ mk$ are perpendicular to each other. Then, the value of $m$ will be :
If two vectors $\vec{P}=\hat{i}+2 m \hat{j}+m \hat{k}$ and $\vec{Q}=4 \hat{i}-2 \hat{j}+ mk$ are perpendicular to each other. Then, the value of $m$ will be :
- [JEE MAIN 2023]
If $\left| {\vec A } \right|\, = \,2$ and $\left| {\vec B } \right|\, = \,4$ then match the relation in Column $-I$ with the angle $\theta $ between $\vec A$ and $\vec B$ in Column $-II$.
Column $-I$
Column $-II$
$(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$
$(i)$ $\theta = \,{0^o}$
$(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$
$(ii)$ $\theta = \,{90^o}$
$(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$
$(iii)$ $\theta = \,{180^o}$
$(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$
$(iv)$ $\theta = \,{60^o}$
If $\left| {\vec A } \right|\, = \,2$ and $\left| {\vec B } \right|\, = \,4$ then match the relation in Column $-I$ with the angle $\theta $ between $\vec A$ and $\vec B$ in Column $-II$.
| Column $-I$ | Column $-II$ |
| $(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$ | $(i)$ $\theta = \,{0^o}$ |
| $(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$ | $(ii)$ $\theta = \,{90^o}$ |
| $(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$ | $(iii)$ $\theta = \,{180^o}$ |
| $(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$ | $(iv)$ $\theta = \,{60^o}$ |
When $\vec A.\vec B = - |A||B|,$ then
When $\vec A.\vec B = - |A||B|,$ then