Given : $\vec A\, = \,2\hat i\, + \,p\hat j\, + q\hat k$ and $\vec B\, = \,5\hat i\, + \,7\hat j\, + 3\hat k,$ if $\vec A\,||\,\vec B,$ then the values of $p$ and $q$ are, respectively
- A$\frac {14}{5}$ and $\frac {6}{5}$
- B$\frac {14}{3}$ and $\frac {6}{5}$
- C$\frac {6}{5}$ and $\frac {1}{3}$
- D$\frac {3}{4}$ and $\frac {1}{4}$
Similar Questions
The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ....... $^o$
The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ....... $^o$
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Define the scalar product of two vectors.
If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $......m$.
If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $......m$.
- [JEE MAIN 2022]
Find the angle between two vectors $\vec A = 2\hat i + \hat j - \hat k$ and $\vec B = \hat i - \hat k$ ....... $^o$
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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 |