( a b ) [ ( b c ) ( a b + b c + c a ) ] is - Vidyadip

MCQ

$\left( {\vec a \times \vec b} \right) \times \left[ {\left( {\vec b \times \vec c} \right) \times \left( {\vec a \times \vec b + \vec b \times \vec c + \vec c \times \vec a} \right)} \right]$ is

A
$\left[ {\vec a\,\vec b\,\vec c} \right]\left[ {\left( {\vec b \cdot \vec a + \vec a \cdot \vec c} \right)\vec b - \left( {{{\left| {\vec b} \right|}^2} + \vec b \cdot \vec c} \right)\vec a} \right]$
B
$\left[ {\vec a\,\vec b\,\vec c} \right]\left[ {\left( {\vec b \cdot \vec a + \vec a \cdot \vec c} \right)\vec b + \left( {{{\left| {\vec b} \right|}^2} - \vec b \cdot \vec c} \right)\vec a} \right]$
C
$\left[ {\vec a\,\vec b\,\vec c} \right]\left[ {\left( {\vec b \cdot \vec a - \vec a \cdot \vec c} \right)\vec b + \left( {{{\left| {\vec b} \right|}^2} + \vec b \cdot \vec c} \right)\vec a} \right]$
✓
$\left[ {\vec a\,\vec b\,\vec c} \right]\left[ {\left( {\vec a \cdot \vec c - \vec b \cdot \vec a} \right)\vec b + \left( {{{\left| {\vec b} \right|}^2} - \vec b \cdot \vec c} \right)\vec a} \right]$

✓

Answer

Correct option: D.

$\left[ {\vec a\,\vec b\,\vec c} \right]\left[ {\left( {\vec a \cdot \vec c - \vec b \cdot \vec a} \right)\vec b + \left( {{{\left| {\vec b} \right|}^2} - \vec b \cdot \vec c} \right)\vec a} \right]$

d
$(\vec{a} \times \vec{b}) \times(-\vec{b} \vec{c} \vec{a}] \vec{b}+[\vec{b} \vec{c} \vec{a}] \vec{c})$

$=[\vec{b} \vec{c} \vec{a}]\left(-(\vec{a} \cdot \vec{b}) \vec{b}+|\vec{b}|^{2} \vec{a}+(\vec{a} \cdot \vec{c}) \vec{b}-(\vec{b} \cdot \vec{c}) \vec{a}\right)$

$=[\vec{a} \vec{b} \vec{c}]\left[(\vec{a} \cdot \vec{c}-\vec{b} \cdot \vec{a}) \vec{b}+\left(|\vec{b}|^{2}-\vec{b} \cdot \vec{c}\right) \vec{a}\right]$

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 $S=\{1,2,3,4,5,6,7,8,9,10\}$. Define $f: S \rightarrow S$ as $f(n)=\left\{\begin{array}{cc}2 n, & \text { if } n=1,2,3,4,5 \\ 2 n-11 & \text { if } n=6,7,8,9,10\end{array}\right.$. Let $g : S \rightarrow S$ be a function such that $f o g(n)=\left\{\begin{array}{ll}n+1 & \text {, if } n \text { is odd } \\ n-1 & \text {, if } n \text { is even }\end{array}\right.$, then $g (10)(( g (1)+ g (2)+ g (3)+ g (4)+ g (5))$ is equal to

If ${u^2} = {(x - a)^2} + {(y - b)^2} + {(z - c)^2}$, then $\sum {{{\partial ^2}u} \over {\partial {x^2}}} = $

Directions: In the following questions, the Assertions $(A)$ and Reason$(s)\ (R)$ have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion $(A)$ if $\text{y}=\tan5\text{x}^\circ,$ then $\frac{\text{dy}}{\text{dx}}=\frac{5\pi}{180}\sec^2(5\text{x}^\circ)$
Reason$(R) \pi^\text{c}=90^\circ$

The area bounded by the curves $y = \cos x$ and $y = \sin x$ between the ordinates $x = 0$ and $x = \frac{{3\pi }}{2}$ is :

Function $f(x) = {{4{x^2} + 1} \over x}$ is decreasing for interval

The value of the integral $\int\limits^{\frac{\pi}{2}}_0\frac{\sqrt{\cos\text{x}}}{\sqrt{\cos\text{x}}+\sqrt{\sin\text{x}}}\text{ dx}$ is:

The solution of $y' = 1 + x + {y^2} + x{y^2}$, $y(0) = 0$ is

If $f ( a + b - x )= f ( x ),$ then $\int_{a}^{b} x f(x) d x$ is equal to

In which interval $f(x) = 2x^2 - \ln |x| ,$ $(x \ne 0)$ is monotonically decreasing -

Let $p$ a non singular matrix $1 + p + {p^2} + .... + {p^n} = O$ ($O$ denotes the null matrix), then ${p^{ - 1}} = $