If a + b + c = 0, then which relation is correct - Vidyadip

MCQ

If $a + b + c = 0,$ then which relation is correct

A
$a = b = c = 0$
B
$a\,.\,b = b\,.\,c = c\,.\,a$
✓
$a \times b = b \times c = c \times a$
D
None of these

✓

Answer

Correct option: C.

$a \times b = b \times c = c \times a$

c
(c) Since $a + b + c = 0$

$ \Rightarrow a \times (a + b + c) = 0 \Rightarrow a \times a + a \times b + a \times c = 0$

$ \Rightarrow a \times b = - a \times c = c \times a$ .....$(i)$

Similarly, $b \times (a + b + c) = 0$$ \Rightarrow a \times b = b \times c$.....$(ii)$

By $(i)$ and $(ii),$ we get $a \times b = b \times c = c \times a.$

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 $y = {\tan ^{ - 1}}\sqrt {{{1 + \cos x} \over {1 - \cos x}}} $, then ${{dy} \over {dx}}$ is equal to

$\int_{}^{} {[\sin (\log x) + \cos (\log x)]} \;dx = $

If $\vec a = \hat i - 2\hat j + 3\hat k,\,\,\vec b = 2\hat i + 3\hat j - \hat k\,$ and $\vec c = r\hat i + \hat j + (2r - 1\hat k)\,$ are three vectors such that $\vec c$ is parallel to the plane of $\vec a$ and $\vec b ,$ then $r$ is equal to

If $f(x)$ is a non-zero polynomial of degree four, having local extreme points at $x = -1, 0, 1;$ then the set $S = \{x \in R; f(x) = f(0)\}$ contains exactly

Let $v$ be the solution of the differential equation $\left(1-x^{2}\right) d y=\left(xy+\left(x^{3}+2\right) \sqrt{1-x^{2}}\right) d x,-1 < x < 1$ and $y(0)=0$ if $\int\limits_{-\frac{1}{2}}^{\frac{1}{2}} \sqrt{1-x^{2}} y(x) d x=k$ then $k^{-1}$ is equal to:

The area bounded by the curve $\left| y \right| + \frac{1}{2} = {e^{ - \left| x \right|}}$ is

The domain of the function $f(x){ = ^{16 - x}}{\kern 1pt} {C_{2x - 1}}{ + ^{20 - 3x}}{\kern 1pt} {P_{4x - 5}}$, where the symbols have their usual meanings, is the set

The determinant $\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right|$ is not equal to

If $A$ is any skew $-$ symmetric matrix of odd order then $∣A∣$ equals:

The value of $\int_{\,0}^{\,\sqrt 2 } {[{x^2}]\,dx} ,$ where $[.]$ is the greatest integer function