MCQ
If $a = 2i + 4j + 2k$ and $b = 8i - 3j + \lambda k$ and $a\, \bot \,b,$ then value of $\lambda $ will be
  • A
    $2$
  • B
    $-1$
  • $-2$
  • D
    $1$

Answer

Correct option: C.
$-2$
c
(c)  Clearly, $8 \times 2 - 3 \times 4 + 2 \times \lambda = 0 \Rightarrow \lambda = - 2.$

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

The radius of a cylinder is increasing at the rate of $3\,\,m/sec$ and its altitude is decreasing at the rate of $4 \,m/sec$. The rate of change of volume when radius is  $ 4 $ metres and altitude is  $6 $ metres is
The xy-plane divided the line joining the point (-1, 3, 4) and (2, -5, 6)
  1. Internally in the ratio 2 : 3
  2. Externally in the ratio 2 : 3
  3. Internally in the ratio 3 : 2
  4. Externally in the ratio 3 : 2
If $A$ and $B$ are same order skew symmetric matrices then, $( AB )^{\prime}=$ ___________ .
The angle between the straight lines $\frac{\text{x}+1}{2}=\frac{\text{y}-2}{5}=\frac{\text{z}+3}{4}$ and $\frac{\text{x}-1}{1}=\frac{\text{y}+2}{2}=\frac{\text{z}-3}{-3}$ is:
The distance of the point P(a, b, c) from the x-axis is:
  1. $\sqrt{\text{b}^2+\text{c}^2}$
  2. $\sqrt{\text{a}^2+\text{c}^2}$
  3. $\sqrt{\text{a}^2+\text{b}^2}$
  4. $\text{none of these}$
The determinant $\left| {\begin{array}{*{20}{c}}{{b_1}\, + \,\,{c_1}}&{{c_1}\, + \,\,{a_1}}&{{a_1}\, + \,\,{b_1}}\\{{b_2}\, + \,\,{c_2}}&{{c_2}\, + \,\,{a_2}}&{{a_2}\, + \,\,{b_2}}\\{{b_3}\, + \,\,{c_3}}&{{c_3}\, + \,\,{a_3}}&{{a_3}\, + \,\,{b_3}} \end{array}} \right|$ $=$
Value of $\int\frac{\text{dx}}{\sqrt{2\text{x}-\text{x}^2}}$
  1. $\sin^{-1}(\text{x}-1)+\text{c}$
  2. $\sin^{-1}(1+\text{x})+\text{c}$
  3. $\sin^{-1}(1+\text{x}^2)+\text{c}$
  4. $-\sqrt{2\text{x}-\text{x}^2}+\text{c}$
The function $f(x)=x^3-3 x^2+12 x-18$ is :
The vertices of a triangle are $(0, 0), (x, cos x)$ and $(sin^3x, 0)$ where $0 < x <\frac{\pi}{2}$. The maximum area for such a triangle in sq. units, is
Let $A=\{-4,-3,-2,0,1,3,4\}$ and $R =\{( a , b ) \in A$ $\times A : b =| a |$ or $\left.b ^2= a +1\right\}$ be a relation on $A$. Then the minimum number of elements, that must be added to the relation $R$ so that it becomes reflexive and symmetric, is $........$.