Download App

Scalar Triple Product — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsScalar Triple Product1 Mark
MCQ
If $\vec{\text{r}}.\vec{\text{a}}=\vec{\text{r}}.\vec{\text{b}}=\vec{\text{r}}.\vec{\text{c}}=0$ for some non-zero vector $\vec{\text{r}},$ then the value of $\big[\vec{\text{a}}\vec{\text{ b }}\vec{\text{c}}\big],$ is:
  • A
    2
  • B
    3
  • ✓
    0
  • D
    None of these
✓

Answer

Correct option: C.
0
If $\vec{\text{r}}.\vec{\text{a}}=0$ for some non-zero vector $\vec{\text{r}},$ then either $\vec{\text{a}}$ is a zero - vector or it is perpendicular to $\vec{\text{r}}.$
If one of $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ is zero, then $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]=0$

If all $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ are non - zero, then they must be coplanar as they are perpendicular to vector $\vec{\text{r}}.$

$\therefore\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{c}}\big]=0$

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 Scalar Triple Product→Scalar Triple Product — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int_0^1 {{e^{{x^2}}}(x - \alpha )\,dx = 0,} $ then
→
Function $f(x)=2 x^3-9 x^2+12 x+29$ is monotonically decreasing when:
→
$\frac{\text{x}}{\text{dx}}\int\text{f(x)}\text{dx}$ is equal to:
→
If$f(x) = \left\{ \begin{array}{l}\frac{{|x - a|}}{{x - a}},{\rm{when\,\,}}\,x \ne a\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = a\end{array} \right.$,then
→
Given that matrices $A$ and $B$ are of order $3 \times n$ and $m \times 5$ respectively, then the order of matrix $C=5 A+3 B$ is
→
The inverse matrix of $\left[ {\begin{array}{*{20}{c}}0&1&2\\1&2&3\\3&1&1\end{array}} \right],$ is
→
The differential equation for all the straight lines which are at a unit distance from the origin is
→
Let $A=\left[\begin{array}{cc}0 & -2 \\ 2 & 0\end{array}\right]$. If $M$ and $N$ are two matrices given by $M =\sum \limits_{ k =1}^{10} A ^{2 k }$ and $N =\sum \limits_{ k =1}^{10} A ^{2 k -1}$ then $MN ^{2}$ is
→
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is:
→
The differential coefficient of $f[\log (x)]$ when $f(x) = \log x$ is
→