Download App

VECTOR ALGEBRA — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsVECTOR ALGEBRA1 Mark
Question
If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ are non-coplanar vectors, then $\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$ is equal to:
  1. 0
  2. 2
  3. 1
  4. None of these
✓

Answer

  1. 0

Solution:

We have

$\frac{\vec{\text{a}}.\big(\vec{\text{b}}\times\vec{\text{c}}\big)}{\big(\vec{\text{c}}\times\vec{\text{a}}\big).\vec{\text{b}}}+\frac{\vec{\text{b}}.\big(\vec{\text{a}}\times\vec{\text{c}}\big)}{\vec{\text{c}}.\big(\vec{\text{a}}\times\vec{\text{b}}\big)}$

$\frac{\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]}{\big[\vec{\text{c}}\vec{\text{a}}\vec{\text{b}}\big]}+\frac{\big[\vec{\text{b}}\vec{\text{a}}\vec{\text{c}}\big]}{\big[\vec{\text{c}}\vec{\text{a}}\vec{\text{b}}\big]}$ (By definition of scalar tiple product)

$=\frac{\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]}{\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]}+\frac{-\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]}{\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]}$ (Change in cyclic order of vectors changes the sign of the scalar triple product)

$=1-1$

$=0$

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

If the position vectors of  $ A $ and $B$  be $6i + j - 3k$ and $4i - 3j - 2k,$ then the work done by the force $\vec F = i -3 j + 5k$ in displacing a particle from $A$  to $ B $ is ............ $\mathrm{unit}$
→
Let $\alpha $ and $\beta $ be the roots of the equation $x^2 + x + 1 = 0.$ Then for $y \ne 0$ in $R,$ $\left| {\begin{array}{*{20}{c}}
{y\, + \,1}&\alpha &\beta \\
\alpha &{y\, + \,\beta }&1\\
\beta &1&{y\, + \,\alpha }
\end{array}} \right|$ is equal to
→
The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is
→
Which of the following is the integrating factor of $(\text{x}\log\text{x})\frac{\text{dy}}{\text{dx}}+\text{y}=2\log\text{x}?$
  1. $\text{x}$ 
  2. $\text{e}^{\text{x}}$
  3. $\log\text{x}$
  4. $\log(\log\text{x})$
→
If A and B are two matrices of order 3×m and 3×n respectively and m = n, then the order of 5A - 2B is:
  1. m×3
  2. 3×3
  3. m×n
  4. 3×n
→
If $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},\text{J}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\cos\theta&\sin\theta\\-\sin\theta&\cos\theta\end{bmatrix},$ then B equals:
  1. $\text{I}\cos\theta+\text{J}\sin\theta$
  2. $\text{I}\sin\theta+\text{J}\cos\theta$
  3. $\text{I}\cos\theta-\text{J}\sin\theta$
  4. $-\text{I}\cos\theta+\text{J}\sin\theta$
→
The equation of the plane containing the lines $r = {a_1} + \lambda {a_2}$ and $r = {a_2} + \lambda {a_1}$ is
→
$2{\tan ^{ - 1}}\left( {\frac{1}{3}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $
→
Let a function $f:[0,5] \rightarrow \mathrm{R}$ be continuous. $f(1)=3$ and $\mathrm{F}$ be defined as

$\mathrm{F}(\mathrm{x})=\int\limits_{1}^{\mathrm{x}} \mathrm{t}^{2} \mathrm{g}(\mathrm{t}) \mathrm{dt},$ where $\mathrm{g}(\mathrm{t})=\int\limits_{1}^{\mathrm{t}} \mathrm{f}(\mathrm{u}) \mathrm{du}$

Then for the function $\mathrm{F}$, the point $\mathrm{x}=1$ is 

→
A man takes a step forward with probability $0.4$ and backward with probability $0.6.$ The probability that at the end of eleven steps he is one step away from the starting point is
→