If two vectors $2\hat i + 3\hat j - \hat k$ and $ - 4\hat i - 6\hat j + \lambda \hat k$ are parallel to each other then value of $\lambda$ be
- A$0$
- B$2$
- C$3$
- D$4$
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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
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A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}$ and is parallel to $\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$. The $\mathrm{x}$ and $y$ components of this vector in first quadrant are $\mathrm{x}$ and $3$ respectively where $X$=_____.
A vector has magnitude same as that of $\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}$ and is parallel to $\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$. The $\mathrm{x}$ and $y$ components of this vector in first quadrant are $\mathrm{x}$ and $3$ respectively where $X$=_____.
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What is the product of two vectors if they are parallel or antiparallel ?
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Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
Two adjacent sides of a parallelogram are represented by the two vectors $\hat i + 2\hat j + 3\hat k$ and $3\hat i - 2\hat j + \hat k$. What is the area of parallelogram
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 $-II$ |
| $(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$ | $(i)$ $\theta = \,{30^o}$ |
| $(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$ | $(ii)$ $\theta = \,{45^o}$ |
| $(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$ | $(iii)$ $\theta = \,{90^o}$ |
| $(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$ | $(iv)$ $\theta = \,{0^o}$ |