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 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

The solution of the differential equation $\frac{{dy}}{{dx}} + y = \cos x$ is

The mean and variance of a binomial distribution are $4$ and $3$ respectively, then the probability of getting exactly six successes in this distribution is

Let $3\sin(\text{xy})+4\cos(\text{xy})=5,$ then $\frac{\text{dy}}{\text{dx}}=$

$-\frac{\text{y}}{\text{x}}$
$\frac{3\sin(\text{xy})+4\cos(\text{xy})}{3\cos(\text{xy})-4\sin(\text{xy})}$
$\frac{3\cos(\text{xy})+4\sin(\text{xy})}{4\cos(\text{xy})-3\sin(\text{xy})}$
$\text{None of these.}$

If $\sin y=x \cos (a+y)$, then $\frac{d x}{d y}$ :

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p.q > 0.

Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:

A fair $n(n > 1)$ faces die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{ n }{9}$, then $n$ is equal to

The value of $p$ for which the vectors $2 \hat{i}+p \hat{j}+\hat{k}$ and $-4 \hat{i}-6 \hat{j}+26 \hat{k}$ are perpendicular to each other, is :

A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, then probability that both are dead is

$\int \frac{1-\cos x}{1+\cos x} d x=$ __________ + C .

If f : R → R defind by $\text{f(x)}=\frac{2\text{x}-7}{4}$ is an invertible function, then find f^-1.

$\frac{4\text{x}+5}{2}$
$\frac{4\text{x}+7}{2}$
$\frac{3\text{x}+2}{2}$
$\frac{9\text{x}+3}{5}$