Basic concepts of vector - class-XI
Description: basic concepts of vector | |
Number of Questions: 29 | |
Created by: Ashok Pandey | |
Tags: addition of vectors vector algebra - i vector vector algebra vectors and transformations maths vectors vectors, lines and planes applications of vector algebra |
If $\overrightarrow A ,\overrightarrow B $ and $\overrightarrow C $ are vectors such that $\left| {\overrightarrow B } \right| = \left| {\overrightarrow C } \right|$ , then $\left{ {\left( {\overrightarrow A + \overrightarrow B } \right)} \right. \times \left. {\left( {\overrightarrow A + \overrightarrow C } \right)} \right} \times \left( {\overrightarrow B \times \overrightarrow C } \right).\left( {\overrightarrow B + \overrightarrow C } \right) = 1 $ these relation is ?
If the vectors $\overrightarrow a = \left( {2,{{\log } _3}x,\;a} \right)$ $and\;\overrightarrow b = \left( { - 3,a{{\log } _3}x,{{\log } _3}x} \right)$ are included at an acute angle then-
If $\displaystyle a\times b=a\times c,a\neq 0,$ then
$\displaystyle a\times \left ( b+c \right )+b\times \left ( c+a \right )+c\times \left ( a+b \right )$ is equal to
Let $\displaystyle a=i+j$ and $\displaystyle b=2i-k,$ the point of intersection of the lines $\displaystyle r\times a=b\times a $ and $\displaystyle r\times b=a\times b $ is
If $\overline{a},\overline{b},\overline{c}$ are three non-zero vectors and $\overline{a}\neq\overline{b}$, $\overline{a}\times\overline{c}=\overline{b}\times\overline{c}$, then
If $a +2b +3c = 0$, then $a \times b + b\times c + c\times a = ka\times b,$
Where $k$ is equal to ?
If $\left| \vec { a } \right| =1,\ \left| \vec { b } \right| =2,\ (\vec { a },\vec { b })=\dfrac{2\pi}{3}$ then $\left{(\vec { a } +3\vec { b } )\times \left( 3\vec { a } -\vec { b } \right) \right}^{2}=$
If $\vec a = \hat i + \hat j + \hat k,\,\vec b = \hat i + \hat j,\,\,\hat c = \hat i$ and $\left( {\vec a \times \vec b} \right) \times \vec c = \lambda \vec a \times \mu \vec b$ then $\lambda + \mu $
Let $\vec{a} = \widehat{i} + \widehat{j}$, $\vec{b} = 2 \widehat{i} - \widehat{k}$, then vector $\vec{r}$ satisfying the equations $\vec{r} \times \vec{a} = \vec{b} \times \vec{a}$ and $\vec{r} \times \vec{b} = \vec{a} \times \vec{b}$ is
If the vector $\bar{c}, \bar{a} = x\bar{i}+y\bar{j}+ z\bar{k}, \bar{b}= \bar{j}$ are such that $\bar{a}, \bar{c}, \bar{b}$ from R.H.S then $\bar{c}$ =
If $a,b,c$ are unit vectors, then the maximum value of $|a+2b|^{2}+|b+3c|^{2}+|c+4a|^{2}$ is
If $\displaystyle \bar{a}+p\bar{b}+q\bar{c}=0 $ then
If the vector $a, b$ and $c$ form the sides $BC, CA $ and $AB $ and equal magnitute respectively of a triangle $ABC,$ then
If $\displaystyle a\cdot b=a\cdot c$ and $\displaystyle a\times b=a\times c,$ then
Let $\displaystyle \vec{a}=\hat{i}+\hat{j}$ & $\displaystyle \vec{b}=2\hat{i}+\hat{j}$ The point of intersection of the lines $\displaystyle \vec{r}\times \vec{a}=\vec{b}\times \vec{a}& \vec{r}\times \vec{b}=\vec{a}\times \vec{b}$ is
Let $\displaystyle \vec{A}=2\vec{i}+\vec{k},\,\vec{B}=\vec{i}+\vec{j}+\vec{k},$ and $\displaystyle \vec{C}=4\vec{i}-3\vec{j}+7\vec{k}$ Determine a vector $\displaystyle \vec{R}$satisfying $\displaystyle \vec{R}\times \vec{B}=\vec{C}\times \vec{B}$ and $\displaystyle \vec{R}.\vec{A}=0$
Unit vector $\vec r$ which satisfies $\vec r \times \vec b = \vec r \times \vec c$ where $\vec b = \widehat i + 2 \widehat j + \widehat k $ & $ \vec c = 3 \widehat i + 2 \widehat k $, is
Let $\vec a = \widehat i + \widehat j$ and $\vec b = 2 \widehat i - \widehat k$, then the point of intersection of lines $\vec r \times \vec a = \vec b \times \vec a$ and $\vec r \times \vec b = \vec a \times \vec b$ is
If $\overline{a}\times\overline{b}=\overline{b}\times\overline{c}$, then
If three vectors $\overline{a},\overline{b},\ \overline{c}$ are such that $\overline{a}\neq 0$, $\overline{a}\times\overline{b}=2\overline{a}\times\overline{c},\ |\overline{a}|=|\overline{c}|=1,\ |\overline{b}|=4$ and the angle between $|\overline{b}|$ and $|\overline{c}|$ is $\displaystyle \cos^{-1}\frac{1}{4}$, then $\overline{b}-2\overline{c}=\lambda\overline{a}$ where $\lambda$ is equal to
If $\vec{a}\times\vec{b}=\vec{c}\times\vec{d}$ and $\vec{a}\times\vec{c}=\vec{b}\times\vec{d}$, then
If $\vec {a},\vec {b},\ \vec {c}$ are non-zero non-collinear vectors such that $\vec {a}\times\vec {b}=\vec {b}\times\vec {c}=\vec {c}\times\vec {a}$ , then $\vec {a}+\vec {b}+\vec {c}=$
If $\vec {a}\times \vec {b}=\vec {c}\times \vec {d},\vec {a}\times \vec {c}=\vec {b}\times \vec {d}$, then
If $\vec {a}$ and $\vec {b}$ are not perpendicular to each other and $\vec {r}\times\vec {a}=\vec {b}\times\vec {a},\ \vec {r}.\vec {c}=0$, then $\vec {r}$ is equal to
If $a$ and $b$ are two unit vectors inclined at an angle $\dfrac { \pi }{ 3 }$, then $\left{ a\times \left( b+a\times b \right) \right} \cdot b$ is equal to
Let $\vec{\lambda }=\vec{a}\times \left ( \vec{b}+\vec{c} \right )$, $\vec{\mu }=\vec{b}\times \left ( \vec{c}+\vec{a} \right )$ and $\vec{\nu }=\vec{c}\times \left ( \vec{a}+\vec{b} \right )$, then
Let $\vec{r}\times \vec{a}=\vec{b}\times \vec{a}$ and $\vec{r}.\vec{c}=0$, where $\vec{a}\vec{b}\neq 0$, then $\vec{r}$ is equal to
If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are any three vectors in space then $\left ( \overrightarrow{c}+\overrightarrow{b} \right )\times \left ( \overrightarrow{c}+\overrightarrow{a} \right ).\left ( \overrightarrow{c}+\overrightarrow{b}+\overrightarrow{a} \right )$ is equal to