If a,b,c are three coplanar vectors, then [a + b , ,b + c , ,c + … - Vidyadip

MCQ

If $ a,b,c $ are three coplanar vectors, then $[a + b\,\,b + c\,\,c + a] = $

A
$[a b c]$
B
$2 [a b c]$
C
$3 [a b c]$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
(d) $[a + b\,\,b + c\,\,c + a]$$ = [a\,b\,c] + [a\,b\,a] + [a\,c\,c]$

$ + [a\,c\,a] + [b\,b\,c] + [b\,b\,a] + [b\,c\,c] + [b\,c\,a]$

$ = [a\,b\,c] + [b\,c\,a] = 2[a\,b\,c] = 0$, ($a,b,c $ are coplanar).

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The value of $\sum_{k=1}^{13} \frac{1}{\sin \left(\frac{\pi}{4}+\frac{(k-1) \pi}{6}\right) \sin \left(\frac{\pi}{4}+\frac{k \pi}{6}\right)}$ is equal to

Find the equation of the line joining $\mathrm{A}(1,3)$ and $\mathrm{B}(0,0)$ using determinants and find $\mathrm{k}$ if $\mathrm{D}(\mathrm{k}, 0)$ is a point such that area of triangle $\mathrm{ABD}$ is $3 \,\mathrm{sq}$ $\mathrm{units}$.

Let $S\left( \alpha \right) = \left\{ {\left( {x,y} \right):{y^2} \leq x,0 \leq \alpha } \right\}$ and $A(\alpha )$ is area of the regions $S(\alpha )$. If for a $\lambda ,0 < \lambda < 4,A (\lambda ) : A\left( 4 \right)\,=\,2:5$ then $\lambda $ equals

If $z $ is a complex number of unit modulus and argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.

If ${\log _4}5 = a$ and ${\log _5}6 = b,$ then ${\log _3}2$ is equal to

If $A + B + C = {180^o},$ then $\sum {\tan \frac{A}{2}\tan \frac{B}{2} = } $

If $X = \left[ {\begin{array}{*{20}{c}}{ - x}&{ - y}\\z&t\end{array}} \right]$ then transpose of adj $X$ is

Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$ where $a, b, c$ are distinct real numbers such that the matrix $\left[\begin{array}{ccc}\alpha^2 & \alpha & 1 \\1 & 1 & 1 \\a & b & c\end{array}\right]$ is singular. Then the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$

The sum of the series $3 + 33 + 333 + ... + n$ terms is

If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\ldots$ is $\frac{m}{n}$, where $m$ and $n$ are co-prime numbers, then $m + n$ is equal to