(r ,. ,i)^2 + (r ,. ,j)^2 + (r ,. ,k)^2 = - Vidyadip

MCQ

${(r\,.\,i)^2} + {(r\,.\,j)^2} + {(r\,.\,k)^2} = $

A
$3{r^2}$
✓
${r^2}$
C
$0$
D
None of these

✓

Answer

Correct option: B.

${r^2}$

b
(b) Let $r = xi + yj + zk$ $ \Rightarrow r\,.\,i = x,$ $r\,.\,j = y,$ $r\,.\,k = z$

$ \Rightarrow {(r\,.\,i)^2} + {(r\,.\,j)^2} + {(r\,.\,k)^2} = {x^2} + {y^2} + {z^2} = {r^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

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

Area bounded by the curve $\text{y}=\sin\text{x}$ and the x-axis between $\text{x}=0$ and $\text{x}=2\pi$ is:

If $A=\left[\begin{array}{cc}1 & 5 \\ \lambda & 10\end{array}\right], A ^{-1}=\alpha A+\beta I$ and $\alpha+\beta=-2$ then $4 \alpha^2+\beta^2+\lambda^2$ is equal to:

If $\vec a$ and $\vec b$ are non-zero vectors which are linearly dependent such that $\frac{{\left| {\vec a + \vec b} \right|}}{{\left| {\vec a - \vec b} \right|}}\, = \,2,\,\left| {\vec b} \right|\, > \,\left| {\vec a} \right|$ Then

The region represented by the inequalities $\text{x}\geq6,\text{y}\geq2,2\text{x}+\text{y}\leq0,\text{x}\geq0,\text{y}\geq{0}$ is:

If $A=\left[\begin{array}{ll}x & 0 \\ 1 & 1\end{array}\right]$ and $B=\left[\begin{array}{cc}4 & 0 \\ -1 & 1\end{array}\right]$, then value of $x$ for which $A^2=B$ is

The distance between two points $P$ and $Q$ is $d$ and the length of their projections of $PQ$ on the co-ordinate planes are ${d_1},{d_2},{d_3}$. Then $d_1^2 + d_2^2 + d_3^2 = k{d^2}$ where $‘k’$ is

$\int\limits^3_0\frac{3\text{x}+1}{\text{x}^2+9}\text{ dx}=$

The value of p and q for which the function $f ( x )=\left\{\begin{array}{cl}\frac{\sin (p+1) x+\sin x}{x} & , x<0 \\ \frac{q}{x^2} & , x=0 \\ \frac{\sqrt{x+b x^2}-\sqrt{x}}{x^{\frac{3}{2}}} & , x>0\end{array}\right.$ is continuous for all $x \in R$, are

Let $\vec{a}$ and $\vec{b}$ are unit vectors enclosing an angle $\theta$ and $|\vec{a}+\vec{b}|<1$. Which of the following is true?
$(i) \theta=\frac{\pi}{2}$
$(ii) \theta<\frac{\pi}{3}$
$(iii)\pi \geq \theta>\frac{2 \pi}{3}$
$(iv) \cos \theta<-\frac{1}{2}$

If the fucnction $\text{f(x)}=\begin{cases}(\cos\text{x})^{\frac{1}{\text{x}}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ is continuouse at x = 0, then the value of k is: