Vector $P =6 \hat{ i }+4 \sqrt{2} \hat{ j }+4 \sqrt{2} \hat{ k }$ makes angle from $z$-axis equal to
- A$\cos ^{-1}\left(\frac{\sqrt{2}}{5}\right)$
- B$\cos ^{-1}(2 \sqrt{2})$
- C$\cos ^{-1}\left(\frac{2 \sqrt{2}}{5}\right)$
- DNone of these
Similar Questions
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 |
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]
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 $-II$ |
| $(a)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,0$ | $(i)$ $\theta = \,{30^o}$ |
| $(b)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,8$ | $(ii)$ $\theta = \,{45^o}$ |
| $(c)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4$ | $(iii)$ $\theta = \,{90^o}$ |
| $(d)$ $\left| {\vec A \, \times \,\,\vec B } \right|\, = \,\,4\sqrt 2$ | $(iv)$ $\theta = \,{0^o}$ |
What is the angle between $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P \times \overrightarrow Q )$
What is the angle between $(\overrightarrow P + \overrightarrow Q )$ and $(\overrightarrow P \times \overrightarrow Q )$
If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $n$ is . . . . . . ..
If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $n$ is . . . . . . ..
- [JEE MAIN 2024]