If a, b, c be any three non-coplanar vectors, then [a + b , , ,b … - Vidyadip

MCQ

If $a, b, c$ be any three non-coplanar vectors, then $[a + b\,\,\,b + c\,\,\,c + a] = $

A
$|a\,b\,c|$
✓
$2$$[a\,b\,c]$
C
${[\,a\,b\,c\,]^2}$
D
$2\,{[\,a\,b\,c\,]^2}$

✓

Answer

Correct option: B.

$2$$[a\,b\,c]$

b
(b) $[a + b\,\,b + c\,\,c + a] = (a + b).\{ (b + c) \times (c + a)\} $

$ = (a + b).(b \times c + b \times a + c \times c + c \times a)$

$ = (a + b).(b \times c + b \times a + c \times a)$, $\left\{ {\because \,c \times c = 0} \right\}$

$ = a.b \times c + a.b \times a + a.c \times a + b.b \times c$$ + b.b \times a + b.c \times a$

$ = [a\,b\,c] + [b\,c\,a] = 2[a\,b\,c]$.

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 solution of the differential equation, $y\,dx + (x + {x^2}y)dy = 0$ is

Consider $f(x) = [x] + \sqrt {\left\{ X \right\}}$ where $[.]$ denotes greatest integer function and $\{.\}$ denotes fractional part function. Identify the correct statement-

The value of $\sin {47^o} + \sin 61^\circ - \sin 11^\circ - \sin 25^\circ = $

Let $p =99$ and $q =101$. Define $p _1=\log \left(\frac{ p + q }{2}\right)$ and $q _1=\frac{1}{2}(\log p+\log q)$ and $p _2=\log \left(\frac{ p _1+ q _1}{2}\right), \quad q _2=\frac{1}{2}\left(\log p _1+\log q _1\right).$ Where all logarithms have base $10$ . Then

If $2x,\;x + 8,\;3x + 1$ are in $A.P.$, then the value of $x$ will be

A function $f(x)$ is defined as $f(x) =\left[ {\begin{array}{*{20}{c}} {{x^m}\,\sin \,\tfrac{1}{x}}&{x\,\, \ne \,\,0\,,\,\,\,m\,\, \in \,\,N} \\ 0&{if\,\,\,\,\,x\,\, = \,\,0} \end{array}} \right. $ . The least value of $m$ for which $f ‘ (x)$ is continuous at $x = 0$ is

If the chord of contact of tangents from a point on the circle ${x^2} + {y^2} = r_1^2$ to the circle ${x^2} + {y^2} = r_2^2$ touches the circle ${x^2} + {y^2} = r_3^2$, then ${r_1},{r_2},{r_3}$ are in

The volume $V$ and depth $ x $ of water in a vessel are connected by the relation $V = 5x - {{{x^2}} \over 6}$ and the volume of water is increasing at the rate of $5 \, c{m^3}/\sec $, when $x = 2\,cm$. The rate at which the depth of water is increasing, is

If $\int_{}^{} {(\cos x - \sin x)\;dx = \sqrt 2 \sin (x + \alpha ) + c} $, then $\alpha = $

$\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\{{{(a + 1)}^2}}&{{{(b + 1)}^2}}&{{{(c + 1)}^2}}\\{{{(a - 1)}^2}}&{{{(b - 1)}^2}}&{{{(c - 1)}^2}}\end{array}\,} \right| = $