[(a b) (b c) ,(b c) (c a) ,(c a) (a b)] = , - Vidyadip

MCQ

$[(a \times b) \times (b \times c)\,(b \times c) \times (c \times a)\,(c \times a) \times (a \times b)] = \,$

A
${[a\,\,b\,\,c]^2}$
B
${[a\,\,b\,\,c]^3}$
✓
${[a\,\,b\,\,c]^4}$
D
None of these

✓

Answer

Correct option: C.

${[a\,\,b\,\,c]^4}$

c
(c) We have $(a \times b) \times (b \times c)$$ = ((a \times b)\,.\,c)b - ((a \times b)\,.\,b)c = [a\,b\,c]b$

$(b \times c) \times (c \times a) = ((b \times c)\,.\,a)c - ((b \times c)\,.\,c)a = [\,b\,c\,a]\,c$

$(c \times a) \times (a \times b) = ((c \times a)\,.\,b)a - ((c \times a)\,.\,a)b = [c\,a\,b]\,a$

$\therefore \,\,\,[(a \times b) \times (b \times c)(b \times c) \times (c \times a)(c \times a) \times (a \times b)]$

$ = [[a\,b\,c]\,a\,[a\,b\,c]\,b\,[a\,b\,c]\,c]$$ = {[a\,b\,c]^3}[a\,b\,c] = {[a\,b\,c]^4}.$

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 STD 12 - 10. vector algebra→STD 12 - 10. vector algebra — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let three vectors $\overrightarrow{ a }, \overrightarrow{ b }$ and $\overrightarrow{ c }$ be such that $\overrightarrow{ c }$ is coplanar with $\overrightarrow{ a }$ and $\overrightarrow{ b }, \overrightarrow{ a } \cdot \overrightarrow{ c }=7$ and $\overrightarrow{ b }$ is perpendicular to $\overrightarrow{ c },$ where $\overrightarrow{ a }=-\hat{ i }+\hat{ j }+\hat{ k }$ and $\overrightarrow{ b }=2 \hat{ i }+\hat{ k },$ then the value of $2|\overrightarrow{ a }+\overrightarrow{ b }+\overrightarrow{ c }|^{2}$ is .........

The solution of $y\,dx - xdy + 3{x^2}{y^2}{e^{{x^3}}}dx = 0$ is

If m[-3 amp; 4] + n[-3 amp; 4] = [10 amp;-11], then 3m + 7n =

If $\text{x}+\text{y}\leq2,$ $\text{x}\leq0,$ $\text{y}\leq0$ the point at which maximum value of 3x + 2y attained will be.

$\int_{}^{} {\frac{{\log x\;dx}}{{{x^3}}} = } $

Let $\vec{a}=\hat{i}+\hat{j}+2 \hat{k}, \vec{b}=2 \hat{i}-3 \hat{j}+\hat{k}$ and $\overrightarrow{ c }=\hat{ i }-\hat{ j }+\hat{ k }$ be three given vectors. Let $\vec{v}$ be a vector in the plane of $\vec{a}$ and $\overrightarrow{ b }$ whose projection on $\overrightarrow{ c }$ is $\frac{2}{\sqrt{3}}$. If $\overrightarrow{ v } . \hat{ j }=7$, then $\overrightarrow{ v } \cdot(\hat{ i }+\hat{ k })$ is equal to

Evaluate $\begin{bmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{bmatrix}$ is:

Area of the region between the curves $\text{x}^2+\text{y}^2=\pi,\text{y}=\sin\text{x}$ and $y-$axis in first quadrant is:

The length and foot of the perpendicular from the point $(2, -1, 5)$ to the line $\frac{{x - 11}}{{10}} = \frac{{y + 2}}{{ - 4}} = \frac{{z + 8}}{{ - 11}}$ are

Let $a = 2i + j - 2k$ and $b = i + j.$ If c is a vector such that $a\,.\,c = \,|c|,\,\,|c - a|\, = 2\sqrt 2 $and the angle between $(a \times b)$ and c is ${30^o}$, then $|\,(a \times b) \times c|\, = $