Vec{A} is a vector quantity such that |vec{A}|= nonzero constant. Which of following expressions is

English

Gujarati

Hindi

3-1.Vectors

easy

$\vec{A}$ is a vector quantity such that $|\vec{A}|=$ nonzero constant. Which of the following expressions is true for $\vec{A}$ $?$

A

$\overrightarrow{ A }\cdot \overrightarrow{ A }=0$

B

$\overrightarrow{ A } \times \overrightarrow{ A }<0$

C

$\overrightarrow{ A } \times \overrightarrow{ A }=0$

D

$\overrightarrow{ A } \times \overrightarrow{ A }>0$

(JEE MAIN-2022)

Solution

$|\overrightarrow{ A }| \neq 0$

$\overrightarrow{ A } \times \overrightarrow{ A }=|\overrightarrow{ A }||\overrightarrow{ A }| \sin 0^{\circ} \hat{ n }=0$

Standard 11

Physics

Share

Similar Questions

If $\vec A = 2\hat i + \hat j – \hat k,\,\vec B = \hat i + 2\hat j + 3\hat k$ and $\vec C = 6\hat i – 2j – 6\hat k$ then the angle between $(\vec A + \vec B)$ and $\vec C$ wil be ……. $^o$

medium

What is the angle between $\vec A\,\,$ and $\vec B\,\,$ if $\vec A\,\,$ and $\vec B\,\,$ are the adjacent sides of a parallelogran drawn from a common point and the area of the parallelogram is $\frac {AB}{2}$

medium

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

medium

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 $-II$

$(a)$ $\vec A \,.\,\,\vec B \, = \,\,0$ $(i)$ $\theta = \,{0^o}$

$(b)$ $\vec A \,.\,\,\vec B \, = \,\,+8$ $(ii)$ $\theta = \,{90^o}$

$(c)$ $\vec A \,.\,\,\vec B \, = \,\,4$ $(iii)$ $\theta = \,{180^o}$

$(d)$ $\vec A \,.\,\,\vec B \, = \,\,-8$ $(iv)$ $\theta = \,{60^o}$

medium

The area of the parallelogram determined by $A =2 \hat{ i }+\hat{ j }-3 \hat{ k }$ and $B =12 \hat{ j }-2 \hat{ k }$ is approximately

medium