NDA MATHEMATICS QUIZ - 8

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Question 1:

If position vector of a point $\mathrm{A}$ is $\vec{r}=$ $a \vec{i}+b \vec{j}+c \vec{k}$ where $a, b, c$ all are natural numbers it $\bar{X}=\vec{i}+\vec{j}+\vec{k}$ and $\vec{r} \cdot \vec{X}=12$ than number of possible values for $\vec{A}$ will be.

Question 2:

If $\vec{x}, \vec{y}, \vec{z}$ be there non zero, non coplanar vectors than

$\vec{r}=2 \vec{x}-3 \vec{y}+\vec{z}, \vec{r}_{2}=3 \vec{x}-5 \vec{y}+2 \vec{z}$ and

$\bar{r}_{3}=4 \bar{x}-5 \vec{y}+\vec{z}$ are

Question 3:

If $|\vec{a}|=3$ and $|\vec{b}|=2$ and $3 \bar{a}+\bar{b}=\sqrt{85}=1$

than $[|3 \vec{a}+\vec{b}|]^{2}$ equals

Question 4:

If $\vec{b}+\vec{c}, \vec{c}+\vec{a}, \vec{a}+\vec{b}$

$=\mathrm{k}\left[\begin{array}{lll}\vec{a} & \vec{b} & \vec{c}\end{array}\right]$ where $\vec{a}, \vec{b}, \vec{c}$ are three non

coplanar vectors than $\mathrm{k}$ is

Question 5:

If $\vec{a}$ and $\vec{b}$ are unit be vectors and be the angle between then $3 \vec{a} \times 5 \vec{b}$ is a unit vector for.

Question 6:

If mutually perpendicular vectors $\vec{a}, \vec{b}, \vec{c}$ are given by

$\vec{a}=a_{1} \vec{i}+a_{2} \vec{j}+a_{3} \vec{k}$

$\vec{b}=b, \vec{i}+b_{2} \vec{j}+b_{3} \vec{k}$

and $\vec{C}=c_{1} \vec{i}+c_{2} \vec{j}+c_{3} \vec{k}$

then $\left|\begin{array}{lll}a_{1} & a_{2} & a_{3} \\ b_{1} & b_{2} & b_{3} \\ c_{1} & c_{2} & c_{3}\end{array}\right|$ is equal to

Question 7:

$\left|\begin{array}{ccc}b+c & a-b & a \\ c+a & b-c & b \\ a+b & c-a & c\end{array}\right|$ is equal to:

Question 8:

If the matrix $A=$ $\left[\begin{array}{ccc}K & -4 & 2 \\ 3 & 4 & -1 \\ -2 & -3 & 1\end{array}\right]$ is not non-singular then-

Question 9:

If $\left|\begin{array}{ccc}15-x & 7 & 10 \\ 11-3 x & 7 & 16 \\ 7-x & 7 & 13\end{array}\right|=0$ then $x$ is:

Question 10:

If $\mathrm{P}=\left[\begin{array}{cc}a-i & i \\ -i & a-i\end{array}\right]$ where $\mathrm{i}^{2}=-1$ than which of the following is correct?

serach-testwale
x