If a, b and (a+b) are all unit vectors and is the angle between a… - Vidyadip

MCQ

If $\vec{a}, \vec{b}$ and $(\vec{a}+\vec{b})$ are all unit vectors and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$, then the value of $\theta$ is :

✓
$\frac{2 \pi}{3}$
B
$\frac{5 \pi}{6}$
C
$\frac{\pi}{3}$
D
$\frac{\pi}{6}$

✓

Answer

Correct option: A.

$\frac{2 \pi}{3}$

Given, $|\vec{a}|=|\vec{b}|=|\vec{a}+\vec{b}|=1$
Now, $|\vec{a}+\vec{b}|^2=|\vec{a}|^2+|\vec{b}|^2+2|\vec{a}||\vec{b}| \cos \theta$
$\Rightarrow 1^2=1^2+1^2+2 \cdot 1 \cdot 1 \cos \theta$
$\Rightarrow \cos \theta=\frac{-1}{2}$
$\Rightarrow \theta=\cos ^{-1}\left(\frac{-1}{2}\right)$
$\Rightarrow \theta=\frac{2 \pi}{3}$

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

The value of $k$ for which the function $f\left( x \right) = \left\{ \begin{gathered} {\left( {\frac{4}{5}} \right)^{\frac{{\tan \,4x}}{{\tan \,5x}}}},\,\,\,\,0 < x < \frac{\pi }{2} \hfill \\ k + \frac{2}{5}\,\,\,,\,\,\,\,\,\,\,\,\,\,\,x = \frac{\pi }{2} \hfill \\ \end{gathered} \right.$ is continuous at $x\,= \frac{\pi}{2}$ is

Let the numbers $2, b, c$ be in an $A.P$ and $A = \left[ {\begin{array}{*{20}{c}}
1&1&1 \\
2&b&c \\
4&{{b^2}}&{{c^2}}
\end{array}} \right]$. If $det(A) \in [2,16]$ then $c$ lies in the interval

The foci of the curve which satisfies the differential equation $(1 + y^2) dx - xy\, dy = 0$ and passes through the point $(1 , 0)$ are :

Let $f(x) = x^3 + 3x^2 - 9x + 2.$ Then, $f(x)$ has,

If the area above the $x-$ axis, bounded by the curve $y = 2kx$ and $x = 0$, and $x = 2$ is $\frac{3}{\log_{\text{e}}2},$ then the value of $k$ is:

If $'R'$ is the least value of $'a'$ such that the function $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+\mathrm{ax}+1$ is increasing on $[1,2]$ and $'\mathrm{S}^{\prime}$ is the greatest value of $'a'$ such that the function $f(x)=x^{2}+a x+1$ is decreasing on $[1,2]$, then the value of $|\mathrm{R}-\mathrm{S}|$ is ..... .

If $a,\,\,b,\,\,c$ are non-coplanar vectors and $ \lambda$ is a real number, then the vectors $a + 2b + 3c,\,\lambda \,b + 4c$ and $(2\lambda - 1)c$ are non-coplanar for

Let the solution curve $y=y(x)$ of the differential equation $\left(4+x^{2}\right) d y-2 x\left(x^{2}+3 y+4\right) d x=0$ pass through the origin. Then $y(2)$ is equal to

$\int {\frac{{{3^x}}}{{\sqrt {{9^x} - 1} }}\,\,dx = } $

Write the function in the simplest form: $\tan ^{-1}\left(\frac{3 a^{2} x-x^{3}}{a^{3}-3 a x^{2}}\right), a>0 ; \frac{-a}{\sqrt{3}} \leq x \leq \frac{a}{\sqrt{3}}$