The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j - 2\hat k} \right)$ and $\vec B = \left( {5\hat i - 6\hat j - y\hat k} \right)$ may be parallel are
- A$x = 0$, $y = \frac{2}{3}$
- B$x = - \frac{{36}}{5},y = \frac{5}{3}$
- C$x = - \frac{{15}}{3},y = \frac{{23}}{5}$
- D$x = \frac{{36}}{5},y = \frac{{15}}{4}$
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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 $-II$ |
| $(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$ | $(i)$ $\theta = \,{0^o}$ |
| $(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$ | $(ii)$ $\theta = \,{90^o}$ |
| $(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$ | $(iii)$ $\theta = \,{180^o}$ |
| $(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$ | $(iv)$ $\theta = \,{60^o}$ |
Which of the following is not true ? If $\overrightarrow A = 3\hat i + 4\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ where $ A$ and $B$ are the magnitudes of $\overrightarrow A $ and $\overrightarrow B $
Which of the following is not true ? If $\overrightarrow A = 3\hat i + 4\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$ where $ A$ and $B$ are the magnitudes of $\overrightarrow A $ and $\overrightarrow B $
The angle between the vectors $\overrightarrow A $ and $\overrightarrow B $ is $\theta .$ The value of the triple product $\overrightarrow A \,.\,(\overrightarrow B \times \overrightarrow A \,)$ is
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- [AIPMT 2005]