The points represented by a, b, c, d are coplanar and ( A ) a + (… - Vidyadip

MCQ

The points represented by $\vec a,\vec b,\vec c,\vec d$ are coplanar and $\left( {\sin A} \right)\vec a + \left( {2\sin 2B} \right)\vec b + \left( {3\sin 3C} \right)\vec c - 4\vec d = \vec 0$ then the least value of $\frac{{21}}{8}\left( {{{\sin }^2}A + {{\sin }^2}2B + {{\sin }^2}3C} \right)$ is

A
$1$
B
$2$
C
$4$
✓
$3$

✓

Answer

Correct option: D.

$3$

d
clearly $sinA +2sin2B+3sin3C=4$

$⇒$ ${\sin ^2}A + {\sin ^2}2B + {\sin ^2}3C \geqslant \frac{{{4^2}}}{{14}}$

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 slope of the tangent to the curve x = t² + 3 t - 8, y = 2t² - 2t - 5 at point (2, -1) is:

$\frac{22}{7}$
$\frac{6}{7}$
$-6$
$\text{None of these}$

Let $X$ be a binomially distributed random variable with mean $4$ and variance $\frac{4}{3}$. Then $54 P ( X \leq 2)$ is equal to.

The points (k − 1, k + 2), (k, k + 1), (k + 1, k) are collinear for:

any value of k
k = −21 only
no value of k
integral values of k only

If the system of linear equation $x + 2ay + az = 0,$ $x + 3by + bz = 0,$ $x + 4cy + cz = 0$ has a non zero solution, then $a,b,c$

For $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then $14 A^{-1}$ is given by

The set of values of $‘a’$ which satisfy the equation

$\int\limits_0^2 {(t - {{\log }_2}a)\,dt} $ $= log_2$ $\left( {\frac{4}{{{a^2}}}} \right)$ is

$\int\text{e}^{\text{x}}\{\text{f(x)}+\text{f}'(\text{x})\}\text{dx}=$

$\text{e}^{\text{x}}\text{f(x)}+\text{C}$
$\text{e}^{\text{x}}+\text{f(x)}$
$2\text{e}^{\text{x}}\text{f(x)}$
$\text{e}^{\text{x}}-\text{f(x)}$

$A$ relation $R$ is defined from $\{2, 3, 4, 5\}$ to $\{3, 6, 7, 10\}$ by $xRy \Leftrightarrow x$ is relatively prime to $y$. Then domain of $R$ is

Let * be a binary operation defined on Q⁺ by the rule $\text{a}*\text{b}=\frac{\text{ab}}3\forall\text{ a, b}\in \text{Q}^+$. The inverse of 4 * 6 is:

$\frac{9}{8}$
$\frac{2}3$
$\frac{3}2$
None of these.

If $f(x)=x^3+b x^2+c x+d$ and 0 < $b^2$ < c then in the interval $(-\infty, \infty)$ , f(x) is