Download App

STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
If $\left[ {a \times b\;\;b \times c\;\;c \times a} \right] = \alpha \;{\left[ {a\;\;b\;\;c} \right]^2}$ then $\lambda$ is equal to 
  • A
    $0$
  • ✓
    $1$
  • C
    $2$
  • D
    $3$
✓

Answer

Correct option: B.
$1$
b
L. H.S.

$=(\bar{a} \times \bar{b}) \cdot[(\vec{b} \times \vec{c}) \times(\vec{c} \times \vec{a})]$

$=(\vec{a} \times \vec{b}) \cdot[(\vec{b} \times \vec{c} \cdot \vec{a}) \vec{c}-(\vec{b} \times \vec{c} \cdot \vec{c}) \vec{a}]$

$ = (\vec a \times \vec b) \cdot [[\bar b\bar c\bar a]\vec c]\quad [\vec b \times \vec c.\vec c = 0]$

$=[\bar{a} \bar{b} \bar{c}] \cdot(\bar{a} \times \bar{b} \cdot \bar{c})=[\bar{a} \bar{b} \bar{c}]^{2}$

$[\vec{a} \times \vec{b} \vec{b} \times \vec{c} \quad \vec{c} \times \vec{a}]=[\bar{a} \bar{b} \bar{c}]^{2}$

So $\lambda=1$

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

If $\vec{a}, \vec{b}, \overrightarrow{ c }$ are three non-zero vectors and $\hat{ n }$ is a unit vector perpendicular to $\vec{c}$ such that $\overrightarrow{ a }=\alpha \overrightarrow{ b }-\hat{ n },(\alpha \neq 0) \quad$ and $\quad \overrightarrow{ b } \cdot \overrightarrow{ c }=12$, then $|\overrightarrow{ c } \times(\overrightarrow{ a } \times \overrightarrow{ b })|$ is equal to :
→
If a line makes angles $Q_1, Q_{21}$ and $Q_3$ respectively with the coordinate axis then the value of $\cos^2 \text{Q}_{1} + \cos^2 \text{Q}_{2} + \cos^2 \text{Q}_{3}$:
→
Statement $1$ : If the system of equations $x + ky + 3z = 0, 3x+ ky - 2z = 0, 2x + 3y - 4z = 0$ has a nontrivial solution, then the value of $k$ is $\frac{31}{2}$

Statement $2$ : A system of three homogeneous equations in three variables has a non trivial solution if the determinant of the coefficient matrix is zero.

→
$\int_{}^{} {\frac{{{e^x}(x + 1)}}{{{{\cos }^2}(x{e^x})}}dx = } $
→
The solution of the differential equation $(1 + {x^2})\frac{{dy}}{{dx}} = x(1 + {y^2})$ is
→
Area of the region enclosed between the curves $x = y^2 -1$ and $x = |y|$ $\sqrt {1 - {y^2}} $ is
→
Let $f$ be a differentiable function satisfying the relation $f(xy) = xf(y) + yf(x) -2xy$ (where $x,y > 0)$ and $f'(1) = 3$, then 
→
If $x$ satisfies the equation $\left( {\int\limits_0^1 {\frac{{dt}}{{{t^2} + 2t\cos \alpha  + 1}}} } \right)\,{x^2}$ $-$ $\,\left( {\int\limits_{ - 3}^3 {\frac{{{t^2}\sin 2t}}{{{t^2} + 1}}\,dt} } \right)\,x$ $-$ $2$  $ =$ $ 0 (0 < \alpha < \pi ), $ then the value $x$ is
→
The value of $\lim\limits _{n \rightarrow \infty} 6 \tan \left\{\sum\limits_{r=1}^{n} \tan ^{-1}\left(\frac{1}{r^{2}+3 r+3}\right)\right\}$ is equal to
→
The probability that a leap year will have 53 fridays or 53 Saturdays is.
→