Download App

VECTOR ALGEBRA — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSVECTOR ALGEBRA1 Mark
Question
Choose the correct answer from the given four options.
The vectors from origin to the points A and B are $\vec{\text{a}}=2\hat{\text{i}}-3\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}},$ respectively, then the area of the triangle OAB is:
  1. $340$
  2. $\sqrt{25}$
  3. $\sqrt{229}$
  4. $\frac{1}{2}\sqrt{229}$
✓

Answer

  1. $\frac{1}{2}\sqrt{229}$
Solution:
$\therefore$ Area of $\triangle\text{OAB}=\frac{1}{2}|\overrightarrow{\text{OA}}\times\overrightarrow{\text{OB}}|$
$=\frac{1}{2}|(2\hat{\text{i}}-3\hat{\text{j}}+2\hat{\text{k}})\times(2\hat{\text{i}}+3\hat{\text{j}}+\hat{\text{k}})|$
$=\frac{1}{2}\begin{vmatrix}\hat{\text{i}}&\hat{\text{j}}&\hat{\text{k}} \\2&-3&2\\2&3&1 \end{vmatrix}$
$=\frac{1}{2}|[\hat{\text{i}}(-3-6)-\hat{\text{j}}(2-4)+\hat{\text{k}}(6+6)]|$
$=\frac{1}{2}|-9\hat{\text{i}}+2\hat{\text{j}}+12\hat{\text{k}}|$
$\therefore$ Area of $\triangle\text{OAB}=\frac{1}{2}\sqrt{81+4+144}$
$=\frac{1}{2}\sqrt{229}$

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

[-1, 1] is the domain for which of the following inverse trigonometric functions?
  1. $\sin^{-1}\text{⁡x}$
  2. $\cot^{-1}\text{⁡x}$
  3. $\tan^{-1}\text{⁡x}$
  4. $\sec^{-1}\text{⁡x}$
→
If the lengths of projections of a line segment on the axes be respectively $3,4,12$, then the length of the line segment is:
→
The primitive of the function $\text{f(x)}=\Big(1-\frac{1}{\text{x}^2}\Big)\text{a}^{\text{x}+\frac{1}{\text{x}}},\text{ a}>0$ is:
  1. $\frac{\text{a}^{\text{x}+\frac{1}{\text{x}}}}{\log_\text{e}\text{a}}$
  2. $\log_\text{e}\text{a}\cdot\text{a}^{\text{x}+\frac{1}{\text{x}}}$
  3. $\frac{\text{a}^{\text{x}+\frac{1}{\text{x}}}}{\text{x}}{\log_\text{e}\text{a}}$
  4. $\text{x}\frac{\text{a}^{\text{x}+\frac{1}{\text{x}}}}{\log_\text{e}\text{a}}$
→
If A and B are two independent events with $\text{P(A)}=\frac{3}{5}$ and $\text{P(B)}=\frac{4}{9},$ then $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$ equals,
  1. $\frac{4}{15}$
  2. $\frac{8}{45}$
  3. $\frac{1}{3}$
  4. $\frac{2}{9}$
→
If function $f$ is defined such that
$
f(x)=\left\{\begin{array}{cc}
\frac{k \cos x}{\pi-2 x}, & \text { if } x \neq \frac{\pi}{2} \\
3, & \text { if } x=\frac{\pi}{2}
\end{array}\right.
$is continuous at $x=\frac{\pi}{2}$, then value of $k$ :
→
Choose the correct answer from the given four option.
The differential equation for $\text{y}=\text{A}\cos\alpha\text{x}+\text{B}\sin\alpha\text{x},$ where A and B are arbitrary constants is:
  1. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-\alpha^2\text{y}=0$
  2. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\alpha^2\text{y}=0$
  3. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}+\alpha\text{y}=0$
  4. $\frac{\text{d}^2\text{y}}{\text{d}\text{x}^2}-\alpha\text{y}=0$
→
On the set $Q^+$ of all positive rational numbers a binary operation $*$ is defined by $\text{a}*\text{b}=\frac{\text{ab}}2\forall\text{ a, b}\in \text{Q}^+$. The inverse of $8$ is:
→
 Z = 7x + y, subject to $ 5\text{x}+\text{y}\geq5,\text{x}+\text{y}\geq3,\text{x}\geq0, y\geq0.$ The minimum value of Z occurs at:
  1. $(3, 0)$
  2. $\Big(\frac{1}{2},\frac{5}{2}\Big)$
  3. $(7, 0)$
  4. $(0,5)$
→
In a regular hexagon ABCDEF, $\overrightarrow{\text{AB}}=\vec{\text{a}},\ \overrightarrow{\text{BC}}=\vec{\text{b}}$ and $\overrightarrow{\text{CD}}=\vec{\text{c}}$. Then, $\overrightarrow{\text{AE}}=$
  1. $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$
  2. $2\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$
  3. $\vec{\text{b}}+\vec{\text{c}}$
  4. $\vec{\text{a}}+2\vec{\text{b}}+2\vec{\text{c}}$
→
The general solution of the differential equation $x d y-\left(1+x^2\right) d x=d x$ is :
→