Download App

Vector Algebra — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVector Algebra1 Mark
Question
A unit vector along the vector $4 \hat{i}-3 \hat{k}$ is
✓

Answer

$\text {Let } \vec{v}=4 \hat{i}-3 \hat{k}$
$\therefore|\vec{v}|=\sqrt{4^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5$
$\text { Now, } \hat{v}=\text { unit vector along } \vec{v}$
$\quad=\frac{\vec{v}}{|\vec{v}|}=\frac{1}{5}(4 \hat{i}-3 \hat{k})$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Vector Algebra→Vector Algebra — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\text{F}:[1,\infty)\rightarrow[2,\infty)$ is given by $\text{f(x)}=\text{x}+\frac{1}{\text{x}},$ then $f^{-1}(x)$ equals$:$
→
If $\alpha, \beta, \gamma$ are the direction angles of a vector and $\cos \alpha=\frac{14}{15}, \cos \beta=\frac{1}{3}$, then $\cos \gamma=$
→
If $\int\frac{1}{5+4\sin\text{x}}\text{ dx}=\text{A}\tan^{-1}\Big(\text{B}\tan\frac{\pi}{2}+\frac{4}{3}\Big)+\text{C},$ then:
  1. $\text{A}=\frac{2}{3},\text{B}=\frac{5}{3}$
  2. $\text{A}=\frac{1}{3},\text{B}=\frac{2}{3}$
  3. $\text{A}=-\frac{2}{3},\text{B}=\frac{5}{3}$
  4. $\text{A}=\frac{1}{3},\text{B}=-\frac{5}{3}$
→
If $f(x)$ defind by $\text{f(x)}=\begin{cases}\frac{|\text{x}^2-\text{x}|}{\text{x}^2-\text{x}},&\text{x}\neq0,1\\1,&\text{x}=0\\-1,&\text{x}=1\end{cases}$ then $f(x)$ is continuse for all:
→
If $\text{A}=\begin{bmatrix}2&0&-3\\4&3&1\\-5&7&2\end{bmatrix}$ is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is:
  1. $\begin{bmatrix}2&2&-4\\2&3&4\\-4&4&2\end{bmatrix}$
  2. $\begin{bmatrix}2&4&-5\\0&3&7\\-3&1&2\end{bmatrix}$
  3. $\begin{bmatrix}4&4&-8\\4&6&8\\-8&8&4\end{bmatrix}$
  4. $\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$
→
The matrix $\text{A}=\begin{bmatrix}0&-5&8\\5&0&12\\-8&-12&0\end{bmatrix}$ is a:
  1. Diagonal matrix.
  2. Symmetric matrix.
  3. Skew-symmetric matrix.
  4. Scalar matrix.
→
The feasible region of a linear programming problem is bounded. The corresponding objective function is $Z=6 x-7 y$.
The objective function attains $\qquad$ in the feasible region.
→
Choose the correct answer from the given four options.
If A and B are two events such that $\text{P}(\text{A})=\frac{1}{2},\text{P}(\text{B})=\frac{1}{3},$ $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{4},$ then $\text{P}(\text{A}'\cap\text{B}')$ equals:
→
If $P$ is a $3 \times 3$ matrix such that $P^{\prime}=2 P+I$, where $P^{\prime}$ is the transpose of $P$, then
→
The distance of the plane through the intersection of the planes ax + by + cz +d = 0 and lx + my + nz + P = 0 and parallel to the line y = 0, z = 0
→