If r ,. ,i = r ,. ,j = r ,. ,k and |r| , , = 3, then r = - Vidyadip

MCQ

If $r\,.\,i = r\,.\,j = r\,.\,k$ and $|r|\,\, = 3,$ then $r = $

A
$ \pm \,3\,(i + j + k)$
B
$ \pm \,\frac{1}{3}\,(i + j + k)$
C
$ \pm \,\frac{1}{{\sqrt 3 }}\,(i + j + k)$
✓
$ \pm \,\sqrt 3 \,(i + j + k)$

✓

Answer

Correct option: D.

$ \pm \,\sqrt 3 \,(i + j + k)$

d
(d) Let $r = xi + yj + zk.$ Since $r.i = r.j = r.k$

$ \Rightarrow x = y = z$ .....$(i)$

Also $|r| = \sqrt {{x^2} + {y^2} + {z^2}} = 3 \Rightarrow x = \pm \sqrt 3 $, {By $(i)$}

Hence the required vector $r = \pm \sqrt 3 (i + j + k).$

Trick : As the vector $ \pm \sqrt 3 (i + j + k)$ satisfies both the conditions.

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

The difference of the order and the degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+x^4=0$ is:

If $\frac{{dy}}{{dx}} = y + 3 > 0\;,\;y\left( 0 \right) = 2$, then $y\left( {\ln 2} \right)$ is equal to :

If vectors $\vec A = 2i + 3j + 4k$, $\vec B = i + j + 5k$, and $\vec C$ form a left handed system, then $\vec C$ is

The value of $\int_{}^{} {\frac{{{e^x}}}{{{e^x} + 1}}} \,dx$ is

The solution of the differential equation $({x^2} - y{x^2})\frac{{dy}}{{dx}} + {y^2} + x{y^2} = 0$ is

The number of solutions of the equation $\tan^{-1}2\text{x}+\tan^{-1}3\text{x}=\frac{\pi}{4}$ is:

If the lengths of projections of a line segment on the axes be respectively $3,4,12$, then the length of the line segment is:

If $x, y, z$ are not all simultaneously equal to zero, satisfying the system of equations

($\sin 3 \theta ) x - y + z = 0$
($\cos 2 \theta ) x + 4 y + 3 z = 0$
$2 x + 7 y + 7 z = 0$
then the number of principal values of $\theta$ is

If $f(x)=\left\{\begin{array}{l}x, \text { if } x \leq 1 \\ 7, \text { if } x > 1\end{array}\right.,$ then

If $f(x)=\left|\begin{array}{ccc}2 \cos ^4 x & 2 \sin ^4 x & 3+\sin ^2 2 x \\ 3+2 \cos ^4 x & 2 \sin ^4 x & \sin ^2 2 x \\ 2 \cos ^4 x & 3+2 \sin ^4 x & \sin ^2 2 x\end{array}\right|$ then $\frac{1}{5} f^{\prime}(0)$ is equal to ..........................