If |a| , , = 3, , , ,|b| , , = 1, , ,|c| , , = 4 and a + b + c = … - Vidyadip

MCQ

If $|a|\,\, = 3,\,\,\,|b|\,\, = 1,\,\,|c|\,\, = 4$ and $a + b + c = 0,$ then $a\,.\,b + b\,.\,c + c\,.\,a = $

✓
$-13$
B
$-10$
C
$13$
D
$10$

✓

Answer

Correct option: A.

$-13$

a
(a) ${(a + b + c)^2} = 0$

==> $|a{|^2} + |b{|^2} + |c{|^2} + 2\,a.b + 2\,b.c + 2\,c.a = 0$

==> $9 + 1 + 16 + 2(a.b + b.c + c.a) = 0$

==> $a.b + b.c + c.a = - \frac{{26}}{2} = - 13.$

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

If $\frac{{dy}}{{dx}} = \frac{{xy + y}}{{xy + x}}$, then the solution of the differential equation is

If $A, B$ are non-singular square matrices of the same order, then $\left(A B^{-1}\right)^{-1}=$

The maximum value of f = 4x + 3y subject to constraints $\text{x}\geq0,$ $\text{y}\geq0,$ $2\text{x}+3\text{y}\leq18;\text{x}+\text{y}\geq10$ is:

35
36
34
None of these

If $A = \left[ {\begin{array}{*{20}{c}}1&1\\0&1\end{array}} \right]$, then ${A^n} = $

Let $x=2$ be a local minima of the function $f(x)=2 x^4-18 x^2+8 x+12, x \in(-4,4)$. If $M$ is local maximum value of the function $f$ in $(-4,4)$, then $M =$

In equation $3\text{x}-\text{y}\geq3$ and 4x - 4y > 4.

Let $M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]$, where $\alpha$ is a non-zero real number an $N =\sum\limits_{ k =1}^{49} M ^{2 k }$. If $\left( I - M ^{2}\right) N =-2 I$, then the positive integral value of $\alpha$ is

If $y = \frac{{{x^2}}}{{(x - 1)(x - 2)(x - 3)}} + \frac{{2x}}{{(x - 2)(x - 3)}} + \frac{3}{{x - 3}} + 1,$ then $\frac{xy'}{y}$ is equal to (where $y' = \frac{dy}{dx}$ ) -

The position of a moving car at time $t$ is given by $f(t)=a t^{2}+b t+c, t>0,$ where $a, b$ and $c$ are real numbers greater than $1 .$ Then the average speed of the car over the time interval $\left[ t _{1}, t _{2}\right]$ is attained at the point

The value of c in Rolle's theorem for the function f(x) = x³ - 3x in the interval $\big[0,\sqrt3\big]$ is:

$1$
$-1$
$\frac{3}{2}$
$\frac{1}{3}$