Define the scalar product of two vectors.
Define the scalar product of two vectors.
Similar Questions
Let $\vec A\, = \,(\hat i\, + \,\hat j)\,$ and $\vec B\, = \,(2\hat i\, - \,\hat j)\,.$ The magnitude of a coplanar vector $\vec C$ such that $\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B$ is given by
Let $\vec A\, = \,(\hat i\, + \,\hat j)\,$ and $\vec B\, = \,(2\hat i\, - \,\hat j)\,.$ The magnitude of a coplanar vector $\vec C$ such that $\vec A\cdot \vec C\, = \,\vec B\cdot \vec C\, = \vec A\cdot \vec B$ is given by
- [JEE MAIN 2018]
Two vectors $A$ and $B$ have equal magnitude $x$. Angle between them is $60^{\circ}$. Then, match the following two columns.
colum $I$
colum $II$
$(A)$ $|A+B|$
$(p)$ $\frac{\sqrt{3}}{2} x$
$(B)$ $|A-B|$
$(q)$ $x$
$(C)$ $A \cdot B$
$(r)$ $\sqrt{3} x$
$(D)$ $|A \times B|$
$(s)$ None
| colum $I$ | colum $II$ |
| $(A)$ $|A+B|$ | $(p)$ $\frac{\sqrt{3}}{2} x$ |
| $(B)$ $|A-B|$ | $(q)$ $x$ |
| $(C)$ $A \cdot B$ | $(r)$ $\sqrt{3} x$ |
| $(D)$ $|A \times B|$ | $(s)$ None |
Three particles ${P}, {Q}$ and ${R}$ are moving along the vectors ${A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}$ and ${C}=-\hat{{i}}+\hat{{j}}$ respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B} .$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C} .$ The angle between the direction of motion of $P$ and $Q$ is $\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)$. Then the value of $x$ is ...... .
Three particles ${P}, {Q}$ and ${R}$ are moving along the vectors ${A}=\hat{{i}}+\hat{{j}}, {B}=\hat{{j}}+\hat{{k}}$ and ${C}=-\hat{{i}}+\hat{{j}}$ respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B} .$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C} .$ The angle between the direction of motion of $P$ and $Q$ is $\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)$. Then the value of $x$ is ...... .
- [JEE MAIN 2021]
Find unit vector perpendicular to $\vec A$ and $\vec B$ where $\vec A = \hat i - 2\hat j + \hat k$ and $\vec B = \hat i + 2\hat j$
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 $-II$ |
| $(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$ | $(i)$ $\theta = \,{30^o}$ |
| $(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$ | $(ii)$ $\theta = \,{45^o}$ |
| $(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$ | $(iii)$ $\theta = \,{90^o}$ |
| $(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$ | $(iv)$ $\theta = \,{0^o}$ |