${\vec A }$, ${\vec B }$ and ${\vec C }$ are three non-collinear, non co-planar vectors. What can you say about directin of $\vec A \, \times \,\left( {\vec B \, \times \vec {\,C} } \right)$ ?
${\vec A }$, ${\vec B }$ and ${\vec C }$ are three non-collinear, non co-planar vectors. What can you say about directin of $\vec A \, \times \,\left( {\vec B \, \times \vec {\,C} } \right)$ ?
The direction of $(\vec{B} \times \vec{C})$ will be perpendicular to the plane containing $\vec{B}$ and $\vec{C}$. $\vec{A} \times(\vec{B} \times \vec{C})$ will lie in the plane of $\vec{B}$ and $\vec{C}$ and is perpendicular to $\vec{A}$.
Similar Questions
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
Explain the geometrical interpretation of scalar product of two vectors.
Explain the geometrical interpretation of scalar product of two vectors.
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 $-II$ |
| $(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$ | $(i)$ $\theta = \,{30^o}$ |
| $(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$ | $(ii)$ $\theta = \,{45^o}$ |
| $(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$ | $(iii)$ $\theta = \,{90^o}$ |
| $(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$ | $(iv)$ $\theta = \,{0^o}$ |
Vector $A$ is pointing eastwards and vector $B$ northwards. Then, match the following two columns.
Colum $I$
Colum $II$
$(A)$ $(A+B)$
$(p)$ North-east
$(B)$ $(A-B)$
$(q)$ Vertically upwards
$(C)$ $(A \times B)$
$(r)$ Vertically downwards
$(D)$ $(A \times B) \times(A \times B)$
$(s)$ None
| Colum $I$ | Colum $II$ |
| $(A)$ $(A+B)$ | $(p)$ North-east |
| $(B)$ $(A-B)$ | $(q)$ Vertically upwards |
| $(C)$ $(A \times B)$ | $(r)$ Vertically downwards |
| $(D)$ $(A \times B) \times(A \times B)$ | $(s)$ None |
Let $\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5$, and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5$. The value of $\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)$ is
Let $\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5$, and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5$. The value of $\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)$ is
- [JEE MAIN 2019]