Download App

Vector Algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVector Algebra1 Mark
MCQ
$\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big\{\big(\vec{\text{a}}-\vec{\text{b}}\big)\times\big(\vec{\text{a}}-\vec{\text{b}}-\vec{\text{c}}\big)\big\}$ is equal to:
  • A
    $\big(\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
  • B
    $2\big(\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
  • ✓
    $3\big(\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
  • D
    $0$
✓

Answer

Correct option: C.
$3\big(\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big)$
$\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big\{\big(\vec{\text{a}}-\vec{\text{b}}\big)\times\big(\vec{\text{a}}-\vec{\text{b}}-\vec{\text{c}}\big)\big\}$
$=\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big(\vec{\text{a}}\times\vec{\text{a}}-\vec{\text{a}}\times\vec{\text{b}}-\vec{\text{a}}\times\vec{\text{c}}-\vec{\text{b}}\times\vec{\text{a}}+\vec{\text{b}}\times\vec{\text{b}}+\vec{\text{b}}\times\vec{\text{c}}\big)$
$=\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big(-\vec{\text{a}}\times\vec{\text{b}}-\vec{\text{a}}\times\vec{\text{c}}+\vec{\text{a}}\times\vec{\text{b}}+\vec{\text{b}}\times\vec{\text{c}}\big)$
$=\big(\vec{\text{a}}+2\vec{\text{b}}-\vec{\text{c}}\big).\big(-\vec{\text{a}}\times\vec{\text{c}}+\vec{\text{b}}\times\vec{\text{c}}\big)$
$=\big[\text{a}\text{b}\text{c}\big]+2\big[\text{a}\text{b}\text{c}\big]$
$=3\big[\text{a}\text{b}\text{c}\big]$

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 Vector Algebra→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

Let $f(x)=\left\{\begin{array}{cc}x^{3}-x^{2}+10 x-7, & x \leq 1 \\ -2 x+\log _{2}\left(b^{2}-4\right), & x>1\end{array}\right.$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is.
→
$\int\limits^\infty_0\frac{1}{1+\text{e}^\text{x}}\text{dx}$ equals :
→
The value of $c$ so that for all real $x$, the vectors $cxi - 6j + 3k,\,\,xi + 2j + 2cxk$ make an obtuse angle are
→
Area bounded by lines $y = 2 + x,$ $y = 2 - x$ and $x = 2$ is
→
If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then find $A^{-1}$.
→
Consider the system of equations : $a_1 x+b_1 y+c_1 z=0 , a_2 x+b_2 y+c_2 z=0, a_3 x+b_3 y+c_3 z=0,$ if $\begin{vmatrix}\text{a}_1&\text{b}_1&\text{c}_1\\\text{a}_2&\text{b}_2&\text{c}_2\\\text{a}_3&\text{b}_3&\text{c}_3\end{vmatrix}=0,$ then the system has
→
Lef $f:(0, \pi) \rightarrow R$ be a function given by

$f(x)=\left\{\begin{array}{cc}\left(\frac{8}{7}\right)^{\frac{\tan 8 x}{\tan 7 x}}, & 0 < x < \frac{\pi}{2} \\ a-8, & x=\frac{\pi}{2} \\ (1+\mid \cot x)^{\frac{b}{a}|\tan x|}, & \frac{\pi}{2} < x < \pi\end{array}\right.$

Where $a, b \in Z$. If $f$ is continuous at $x=\frac{\pi}{2}$, then $\mathrm{a}^2+\mathrm{b}^2$ is equal to ..........

→
Let $y = f (x)$ and $y = g (x)$ be two differentiable function in $[0,2]$ such that  $f(0) = 3,$ $f(2) = 5$ , $g (0) = 1$ and $g(2) = 2$. If there exist atlellst one $c \in \left( {0,2} \right)$ such that $f'(c)=kg'(c)$,then $k$ must be
→
If the three points $A(1, 6), B(3, −4)$ and $C(x, y)$ are collinear, then the equation satisfying by $x$ and $y$ is:
→
Choose the correct answer from the given four options.
The position vector of the point which divides the join of points $2\vec{\text{a}}-3\vec{\text{b}}$ and $\vec{\text{a}}+\vec{\text{b}}$ in the ratio 3 : 1 is:
→