Introduction to vector algebra - class-XI
| Description: introduction to vector algebra | |
| Number of Questions: 26 | |
| Created by: Tanya Dwivedi | |
| Tags: vectors vectors and transformations maths vector algebra addition of vectors vector algebra - i |
In a square matrix $A$ of order $3$ the elements, $a _{i\ i}s^{'}$ are the sum of the roots of the equation $x^{2}-(a+b)x+ab=0;\ a _{1,\ i+1}s^{'}$ are the product of the roots, $a _{1,\ i-i}s^{'}$ are all unity and the rest of the elements all zero. The value of the det. $(A)$ is equal to
If $(\vec{a}\times\vec{b})^{2}+(\vec{a}.\vec{b})^{2}=144$ and $|\vec{a}|=4,\ |\vec{b}|=$
One of the following is not a vector
Which one of the following is not a scalar quantity?
If a be an unit vector then
If two vectors have the same magnitude and direction regardless of the positions of their initial points, then they are
A line PQ is symbolically written as
A ray has ................ end point/points.
Which of the following symbols represent vectors?
Which of the following expressions represent vectors ?
Which of the following expressions represent vectors ?
State the following statement is true or false
On ethe rectangularcomponent of a viewer of 20m is 10 m .The component is
$[ a \times b \times c ] = 2[ a b c ] ^ { 2 }$
If the position vectors of the vertices of atriangle are $2 \overline { i } - \overline { j } + \overline { k } , \overline { i } - 3 \vec { j } - 5 \overline { k }$ and $3 \vec { i } - 4 \overline { j } - 4 \overline { k }$ then the triangle is
If $\displaystyle {\sec}^{2}A\hat{i}+\hat{j}+\hat{k}$, $\displaystyle \hat{i}+{\sec}^{2}B\hat{j}+\hat{k}$,and $\displaystyle \hat{i}+\hat{j}+{\sec}^{2}C\hat{k}$, are coplanar then $\displaystyle {\cot}^{2}A+{\cot}^{2}B+{\cot}^{2}{C}$ is
Let $\dot{a}$ = $\hat{i}$ + $\hat{j}$ + $\sqrt{2}\hat{k}$
$\dot{b}$ = $b _1\hat{i}$ + $b _2\hat{j}$ + $\sqrt{2}\hat{k}$
$\dot{c}$ = $5\hat{i}$ + $\hat{j}$ + $\sqrt{2}\hat{k}$
& ($\dot{a}$ + $\dot{b}$) is perpendicular to \overrightarrow{c} and projection vector of $\dot{b}$ on $\overrightarrow{a}$ is $\overrightarrow{a}$ then find $\left | \overrightarrow{b} \right |$
Let a=i+j+k and c=j-k . If b is a vector satisfying a×b=c and a.b=3, then find b.
$A$ vector $\vec V$ is inclined at equal angles to axes $OX,OY$ and $OZ$. If $\vec V$ is $6units$, then $\vec V$ is
$\sum _{ i=1 }^{ n }{ \vec { ai } } =\vec { 0 } \quad where\quad |\vec { a\quad i\quad | } =1\forall i$ then the value of $\sum _{ 1\le i }^{ }{ \sum _{ <j\le n }^{ }{ \vec { { a } _{ i } } } } .\vec { { a } _{ j } } $ is
If $ \vec{a} $ and $ \vec{b} $ are two non-collinear unit vectors such that $ |\vec{a}+\vec{b}| = \sqrt{3}, $ find $(2\vec{a}-5\vec{b}).(3\vec{a}+\vec{b}) $
Which of the following can represent a vector?
Direction of zero vector
Which will result in a vector?
What is the value of $p$ for which the vector $p\left( 2\hat { i } -\hat { j } +2\hat { k } \right)$ is of $ 3$ units length?
If $\vec{x}$ and $\vec{y}$ be unit vectors and $\displaystyle |\vec{z}| = \dfrac{2}{\sqrt 7}$ such that $\vec{z} + (\vec{z} \times \vec{x}) = \vec{y}$ and $\theta$ is the angle between $\vec{x}$ and $\vec{z}$, then the value of sin $\theta$ is