Tag: introduction to vector algebra

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Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

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

  1. $0$

  2. $(a+b)^{3}$

  3. $a^{3}-b^{3}$

  4. $(a^{2}+b^{2})$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Given, square matrix $A$ of order $3$ with $a _{ii}= (a+b) $ (sum of roots)

$a _{1 i+1}=a _{12}=ab$  (product of roots)

$a _{1i-1}= a _{10}=1$

$|A|= \begin{vmatrix} (a+b) & 0 & 0 \\ 1 & (a+b) & ab \\ 0 & 0 & (a+b) \end{vmatrix}= (a+b)[(a+b)(a+b)-0]$

$=(a+b)^{3}$

$\therefore $ Option $B$ is correct.


Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

If two vectors have the same magnitude and direction regardless of the positions of their initial points, then they are

  1. Co-initial vectors

  2. Colinear vectors

  3. Equal Vectors

  4. Unit Vector
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 A quantity that has magnitude as well as direction is called a vector.  

or we can say ,
Two vectors are said to be equal if they have the same magnitude and direction, regardless of the positions of their initial points.

Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

Which of the following symbols represent vectors?

  1. $v$

  2. $\vec{AB}$

  3. $\displaystyle \left| v \right| $

  4. $\displaystyle u+\left| v \right| $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The vector is visual representation of a physical quantity that which has the both direction and the magnitude.

And out of these option,
Only option $B$ have the both direction and magnitude.
So, the correct answer is $\vec {AB}$.
Because it has a particular direction from $A$ to $B$ and also have the magnitude.

Multiple choice maths vectors and transformations introduction to vector algebra algebra of vectors operations on vectors

Which of the following expressions represent vectors ?

  1. $v$

  2. $AB$

  3. $\displaystyle \left| v \right| $

  4. $\displaystyle \vec { AB }  $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The vector is visual representation of a physical quantity that which has the both direction and the magnitude.

And out of these option,
Only option $D$ have the both direction and magnitude.
So, the correct answer is $\vec {AB}$.
Because it has a particular direction from $A$ to $B$ and also have the magnitude.