Let a, b, c three unit vectors such that a ^ .b ^ + b ^ .c ^ - a … - Vidyadip

MCQ

Let $\vec a, \vec b, \vec c$ three unit vectors such that $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to - \mathop a\limits^ \to \mathop {.c}\limits^ \to = \frac{3}{2}$ Then the value of $\mathop a\limits^ \to \mathop {.b}\limits^ \to + \mathop b\limits^ \to \mathop {.c}\limits^ \to + \mathop c\limits^ \to \mathop {.a}\limits^ \to $

✓
$\frac{1}{2}$
B
$1$
C
$\frac{3}{2}$
D
$-\frac{1}{2}$

✓

Answer

Correct option: A.

$\frac{1}{2}$

a
$\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}-\vec{a} \cdot \vec{c}=\frac{3}{2}$

$\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=\frac{3}{2}+2 \cdot \overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}$

$=\frac{3}{2}+2 \times \cos 120^{\circ}=1$

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 STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

If $y = {\sin ^{ - 1}}{{\sqrt {(1 + x)} + \sqrt {(1 - x)} } \over 2}$, then ${{dy} \over {dx}} = $

Evaluate : $\int\frac{1}{1+3\sin^2\text{x}+8\cos^2\text{x}}\text{dx}.$

Let $f(x)=\left|(x-1)\left(x^{2}-2 x-3\right)\right|+x-3, x \in R$. If $m$ and $M$ are respectively the number of points of local minimum and local maximum of $f$ in the interval $(0,4)$, then $m + M$ is equal to

If $z = \sec \,(y - ax) + \tan (y + ax),$ then ${{{\partial ^2}z} \over {\partial {x^2}}} - {a^2}{{{\partial ^2}z} \over {\partial {y^2}}} = $

If the system of equations $ax + y + z = 0$, $x + by + z = 0$ and $x + y + cz = 0 $, where $a,b,c \ne 1,$ has a non trivial solution, then the value of $\frac{1}{{1 - a}} + \frac{1}{{1 - b}} + \frac{1}{{1 - c}}$is

The approximate value of $(33)^{\frac{1}{5}}$ is:

$\int_0^\infty {\frac{{{x^2}\,dx}}{{({x^2} + {a^2})({x^2} + {b^2})}}} = $

The value of $\left|\begin{array}{ccc}\lfloor 1 & \lfloor 2 & \lfloor 3 \\ 2\lfloor 2 & 3 \underline{3} & 4\lfloor 4 \\ \lfloor 3 & \lfloor 4 & \lfloor 5\end{array}\right|$ is

Let $\quad \vec{a}=9 \hat{i}-13 \hat{j}+25 \hat{k}, \vec{b}=3 \hat{i}+7 \hat{j}-13 \hat{k} \quad$ and $\overrightarrow{\mathrm{c}}=17 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\hat{\mathrm{k}}$ be three given vectros. If $\overrightarrow{\mathrm{r}}$ is a vector such that $\vec{r} \times \vec{a}=(\vec{b}+\vec{c}) \times \vec{a}$ and $\vec{r} .(\vec{b}-\vec{c})=0$, then $\frac{|593 \vec{r}+67 \vec{a}|^2}{(593)^2}$ is equal to...........

Evaluate the following determinant : $\left|\begin{array}{cc}x & -7 \\ x & 5 x+1\end{array}\right|$