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.If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are three vectors such that $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=\vec{0}$ and $|\vec{\text{a}}|=2,|\vec{\text{b}}|=3$ and $|\vec{\text{c}}|=5,$ then the value of $\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}}$ is:
  1. 0.
  2. 1.
  3. -19.
  4. 38.
✓

Answer

  1. -19.
Solution:
Here, $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=\vec{0}$ and $\vec{\text{a}}^2=4,\vec{\text{b}}^2=9,\vec{\text{c}}^2=25$
$\therefore(\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}})\cdot(\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}})=0$
$\Rightarrow\vec{\text{a}}^2+\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{a}}\cdot\vec{\text{c}}+\vec{\text{b}}\cdot\vec{\text{a}}+\vec{\text{b}}^2+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}}+\vec{\text{c}}\cdot\vec{\text{b}}+\vec{\text{c}}^2=0$
$\Rightarrow\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}+2(\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}})=0$ $[\because\vec{\text{a}}\cdot\vec{\text{b}}=\vec{\text{b}}\cdot\vec{\text{a}}]$
$\Rightarrow4+9+25+2(\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}})=0$
$\Rightarrow\vec{\text{a}}\cdot\vec{\text{b}}+\vec{\text{b}}\cdot\vec{\text{c}}+\vec{\text{c}}\cdot\vec{\text{a}}=0$
$\Rightarrow\frac{-38}{2}=-19$

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

Choose the correct answer in Exercise:
$\text{If}\ \text{f}(\text{x})=\int^{\text{x}}_{0}\text{t}\sin\text{t}\ \text{dt}$, then $\text{f}\text{(x)}$ is
  1. $\cos\text{x}+\text{x}\sin\text{x}$
  2. $\text{x}\sin\text{x}$
  3. $\text{x}\cos\text{x}$
  4. $\sin\text{x}+\text{x}\cos\text{x}$
→
The graph of the inequality $2 x+3 y>6$ is
→
If $P(A)=\left(\frac{1}{2}\right), P(B)=0$, then the value of $P(A / B)$ will be
→
The area bounded by the x - axis, the curve y = f(x) and the lines x = 1, x = b is equal to $\sqrt{\text{b}}^2+1-\sqrt{2}\text{ for}\text{ all}\text{ b}>,\text{then}\text{ f(x)}\text{ is:}$
  1. $\sqrt{\text{x}-1}$
  2. $\sqrt{\text{x}+1}$
  3. $\sqrt{\text{x}^2+1}$
  4. $\text{x}\sqrt{\text{x}-1}$
→
The number of real values of x satisfying the equation $ \tan^{-1}\left(\frac{\text{x}}{1-\text{x}^2}\right)+\tan^{-1}\left(\frac{1}{\text{x}^3}\right)=\frac{3\pi}{4}$, is?
  1. 0
  2. 1
  3. 2
  4. Infinitely many
→
The sum of the squares of sine of the angles made by the line AB with OX, OY, OZ where O is the origin is:
→
For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true?
→
A zero vector has:
  1. Any direction
  2. No direction
  3. Many direction
  4. None of these
→
Find the area of the ellipse $\frac{x^2}{4^2}+\frac{y^2}{9^2}$.
→
Let $f : R \rightarrow R$ be given by $f(x) = [x^2] + [x + 1] - 3$ where $[x]$ denotes the greatest integer less than or equal to $x$. Then$, f(x)$ is:
→