Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
MCQ
Let $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ be three unit vectors, such that $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=1$ and $\vec{\text{a}}$ is perpendicular to $\vec{\text{b}}.$ If $\vec{\text{c}}$ makes angle $\alpha$ and $\beta$ with $\vec{\text{a}}$ and $\vec{\text{b}}$ respectively, then $\cos\alpha+\cos\beta=$
  • A
    $-\frac{3}{2}$
  • B
    $\frac{3}{2}$
  • C
    $1$
  • ✓
    $-1$
✓

Answer

Correct option: D.
$-1$
Given that $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are unit vectors.

So, $|\vec{\text{a}}|=1,\big|\vec{\text{b}}\big|=1$ and $\vec{\text{c}}=1.$

Since $\vec{\text{a}}$ and $\vec{\text{b}}$ are mutually perpendicular,

$\vec{\text{a}}.\vec{\text{b}}=0$

Now,

$\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=1$

$\Rightarrow\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|^2=1$

$\Rightarrow|\vec{\text{a}}|^2+\big|\vec{\text{b}}\big|^2+|\vec{\text{c}}|^2+2\vec{\text{a}}.\vec{\text{b}}+2\vec{\text{b}}.\vec{\text{c}}+2\vec{\text{c}}.\vec{\text{a}}=1$

$\Rightarrow1+1+1+2(0)+2|\vec{\text{a}}|\big|\vec{\text{b}\big|}\cos\beta+2|\vec{\text{c}}||\vec{\text{a}}|\cos\alpha=1$

$\Rightarrow3+2(\cos\alpha+\cos\beta)=1$

$\Rightarrow2(\cos\alpha+\cos\beta)=-2$

$\Rightarrow\cos\alpha+\cos\beta=-1$

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→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int \frac{\sin x}{\sin ^{3} x+\cos ^{3} x} d x=$

$\alpha \log _{\mathrm{e}}|1+\tan \mathrm{x}|+\beta \log _{\mathrm{c}}\left|1-\tan \mathrm{x}+\tan ^{2} \mathrm{x}\right|+\gamma \tan ^{-1}\left(\frac{2 \tan \mathrm{x}-1}{\sqrt{3}}\right)+\mathrm{C}$

when $\mathrm{C}$ is constant of integration, then the value of $18\left(\alpha+\beta+\gamma^{2}\right)$ is .... .

→
$\int {\frac{{p{x^{p + 2q - 1}-qx^{q-1}}}}{{{x^{2p + 2q}} + 2{x^{p + q}} + 1}}dx} $ is equals :-
→
There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable $X$ denote the number of rotten apples. If $\mu$ and $\sigma^2$ represent mean and variance of $X$, respectively, then $10\left(\mu^2+\sigma^2\right)$ is equal to
→
If $A$ satisfies the equation $\text{x}^2-5\text{x}^2+4\text{x}+\lambda=0$ then $A^{-1}$ exists if :
→
If $f(x)$ is a continuous and differentiable function satisfying $f(x).f(f(x)) = x^2 + 1, \, f(1) = 2, \,f'(1) = k$, then the value of $f'(2)$ is
→
In which of the following graphs $x = c$ is the point of inflection .
→
If P and q are the order and degree of the differention $\text{y}\frac{\text{dy}}{\text{dx}}+\text{x}^{3}\frac{\text{d}^{2}\text{y}}{\text{dx}^{3}}+\text{xy}=\cos\text{x}$ then:
→
$\int_0^{\pi /2} {} \log \sin x\,dx = $
→
Let $P$ the point of intersection of the lines $\frac{x-2}{1}=\frac{y-4}{5}=\frac{z-2}{1}$ and $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-3}{2}$. Then, the shortest distance of $\mathrm{P}$ from the line $4 \mathrm{x}=2 \mathrm{y}=\mathrm{z}$ is
→
z = 10x + 25y subject to $0\leq\text{X}\leq3$ and $0\leq\text{X}\leq3,$ $\text{x}+\text{y}\leq5$ then the maximum value of z is:
→