MCQ
$a \times (b \times c)$ is coplanar with
  • $b$  and  $c$
  • B
    $c$  and $ a$
  • C
    $a $ and $b$
  • D
    $a, b$  and $ c$

Answer

Correct option: A.
$b$  and  $c$
a
(a) $b \times c$ is a vector perpendicular to $b,\,c.$ Therefore, $a \times (b \times c)$ is a vector again in plane of $b,\,c.$

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

Similar questions

For the matrix $A=\left[\begin{array}{ll}3 & 2 \\ 1 & 1\end{array}\right]$. find the number $a$ and $b$ such that $A^{2}+a A+b I=0$
If the function f : R → A given by $\text{f(x)}=\frac{\text{x}^2}{\text{x}^2+1}$ is a surjection, then A =
  1. R
  2. [0, 1]
  3. [0, 1)
  4. [0, 1)
$\int\limits^{\pi}_0\frac{1}{1+\sin\text{x}}\text{ dx}$ equals:

  1. $0$

  2. $\frac{1}{2}$

  3. $2$

  4. $\frac{3}{2}$

The degree of the differential equation $\left[1+\left(\frac{d y}{d x}\right)^2\right]^3=\left(\frac{d^2 y}{d x^2}\right)^2$ is
$\smallint \frac{{{{\sin }^2}x{{\cos }^2}x}}{{{{\left( {{{\sin }^5}x + {{\cos }^3}x{{\sin }^2}x + {{\sin }^3}x{{\cos }^2}x + {{\cos }^5}x} \right)}^2}}}dx$
If $\sin^{-1}\Big(\frac{\text{x}^2-\text{y}^2}{\text{x}^2+\text{y}^2}\Big)=\log\text{a}$ then $\frac{\text{dy}}{\text{dx}}$ is equal to:
  1. $\frac{\text{x}^2-\text{y}^2}{\text{x}^2+\text{y}^2}$
  2. $\frac{\text{y}}{\text{x}}$
  3. $\frac{\text{x}}{\text{y}}$
  4. $\text{None of these.}$
Let $A$ be a $3 \times 3$ matrix such that $A^2 -5A+ 7I = 0$.

Statement $-I$ : ${A^{ - 1}} = \frac{1}{7}\left( {5I - A} \right).$

Statement $II$ : the polynomial $A^3 - 2A^2 - 3A + I$ can be reduced to $5\, (A - 4I)$.

If $\theta$ is the angle between two vectors $\vec{\text{a}}$ and $\vec{\text{b}},$ then $\vec{\text{a}}.\vec{\text{b}}\geq0$ only when:
  1. $0<\theta\frac{\pi}{2}$
  2. $0\leq\theta\leq\frac{\pi}{2}$
  3. $0<\theta<\pi$
  4. $0\leq\theta\leq\pi$
Let $\vec{a}=\alpha \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\alpha \hat{k}, \alpha>0$. If the projection of $\vec{a} \times \vec{b}$ on the vector $-\hat{i}+2 \hat{j}-2 \hat{k}$ is $30 ,$ then $\alpha$ is equal to
Let $a_1, a_2, a_3, \ldots \ldots$ be an A.P. If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :