$\vec A$ and $\vec B$ are two vectors and $\theta$ is the angle between them, if $|\vec A \times \vec B|=\sqrt 3(\vec A \cdot \vec B) $ the value of $\theta$ is ......... $^o$
$\vec A$ and $\vec B$ are two vectors and $\theta$ is the angle between them, if $|\vec A \times \vec B|=\sqrt 3(\vec A \cdot \vec B) $ the value of $\theta$ is ......... $^o$
- [AIPMT 2007]
- A
$60$
- B
$45$
- C
$180$
- D
$0$
Similar Questions
The angle between two vectors given by $6\hat i + 6\hat j - 3\hat k$ and $7\hat i + 4\hat j + 4\hat k$ is
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For component of a vector $A =(3 \hat{ i }+4 \hat{ j }-5 \hat{ k })$, match the following colum.
Colum $I$
Colum $II$
$(A)$ $x-$axis
$(p)$ $5\,unit$
$(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$
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$(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$
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$(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$
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| Colum $I$ | Colum $II$ |
| $(A)$ $x-$axis | $(p)$ $5\,unit$ |
| $(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$ | $(q)$ $4\,unit$ |
| $(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$ | $(r)$ $0$ |
| $(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ | $(s)$ None |
$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$
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- [JEE MAIN 2022]
Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
Given $\left| {{\vec A_1}} \right| = 2,\,\left| {{\vec A_2}} \right| = 3$ and $\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 3$. Find the value or $\left| {\left( {{{\vec A}_1} + 2{{\vec A}_2}} \right) \times \left( {3{{\vec A}_1} - 4{{\vec A}_2}} \right)} \right|$
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