Download App

10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
Let $a = i$ be a vector which makes an angle of ${120^o}$ with a unit vector $b$  Then the unit vector $(a + b)$ is
  • A
    $ - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
  • B
    $ - \frac{{\sqrt 3 }}{2}i + \frac{1}{2}j$
  • ✓
    $\frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
  • D
    $\frac{{\sqrt 3 }}{2}i - \frac{1}{2}j$
✓

Answer

Correct option: C.
$\frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$
c
(c) $b = \cos 120^\circ i + \sin 120^\circ j$ or $b = - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j.$

Therefore $a + b = i - \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j = \frac{1}{2}i + \frac{{\sqrt 3 }}{2}j$.

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 10. vector algebra→10. vector algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let the maximum and minimum values of $\left(\sqrt{8 x-x^2-12}-4\right)^2+(x-7)^2, x \in R$ be $M$ and $m$ respectively. Then $\mathrm{M}^2-\mathrm{m}^2$ is equal to ...............
→
If A = $\begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix}$is such that A2 = I, then:
  1. $1 + \alpha^2 + \beta\gamma = 0$
  2. $1 - \alpha^2 + \beta\gamma = 0$
  3. $1 - \alpha^2 - \beta\gamma = 0$
  4. $1 + \alpha^2 - \beta\gamma = 0$
→
Corner points of the feasible region for an $\operatorname{LPP}$ are $(0,2),(3,0),(6,0),(6,8)$ and $(0,5)$

Let $F=4 x+6 y$ be the objective function. Maximum of $F-$ Minimum of $F=.....$

→
Choose the correct answer from the given four options.
If A and B are matrices of same order, then (AB′ – BA′) is a:
  1. Skew symmetric matrix.
  2. Null matrix.
  3. Symmetric matrix.
  4. Unit matrix.
→
Let $f(x) = \int_{\,1}^{\,x} {\sqrt {2 - {t^2}} dt} $. Then real roots of the equation ${x^2} - f'(x) = 0$ are
→
If $A B=A$ and $B A=B$, then
→
Evaluate the following integral: $\int\sec^2\text{xdx:}$
  1. $2\tan\text{x+c}$
  2. $\tan2\text{x}+\text{c}$
  3. $\tan\text{x}+\text{c}$
  4. None of these 
→
Let $f ( x )$ be a polynomial of degree $6$ in $x ,$ in which the coefficient of $x^{6}$ is unity and it has extrema at $x=-1$ and $x=1$. If $\lim _{x \rightarrow 0} \frac{f(x)}{x^{3}}=1,$ then $5 \cdot f (2)$ is equal to .............
→
For linear programming $x+2 y \geq 10,3 x+4 y \leq 24$ and $x \geq 0, y \geq 0 \ldots \ldots \ldots .$ is not the corner point of feasible region.
→
A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied. Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?
  1. $\frac18$
  2. $\frac28$
  3. $\frac38$
  4. $\frac12$
→