MCQ
The expression $\left( {\frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j} \right)$ is a
- ✓Unit vector
- BNull vector
- CVector of magnitude $\sqrt 2 $
- DScalar
✓
Answer
Correct option: A.
Unit vector
a
(a) $\vec P = \frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j$
(a) $\vec P = \frac{1}{{\sqrt 2 }}\hat i + \frac{1}{{\sqrt 2 }}\hat j$
$|\vec P| = \sqrt {{{\left( {\frac{1}{{\sqrt 2 }}} \right)}^2} + {{\left( {\frac{1}{{\sqrt 2 }}} \right)}^2}} = 1$
It is a unit vector.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
An ideal gas with constant heat capacity $C_V=\frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.
→Two particles are moving along two long straight lines, in the same plane, with the same speed $= 20 \,\,cm/s$. The angle between the two lines is $60^o$, and their intersection point is $O$. At a certain moment, the two particles are located at distances $3\,m$ and $4\,m$ from $O$, and are moving towards $O$. Subsequently, the shortest distance between them will be
→A man is standing on a rough $(\mu = 0.5)$ horizontal disc rotating with constant angular velocity of $5$ $rad/sec.$ At what distance from centre should he stand so that he does not slip on the disc?
→Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel. This law was first formulated by
In a simple pendulum, the breaking strength of the string is double the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle $\theta $ with the vertical
→A boy prevents fall of his book on the ground by pressing it against a vertical wall. If weight of his book is $10\ kg$ and us of the wall is $0.2.$ Find the minimum force needed by him in his attempt.
→An ice block is melting at a constant rate $\left| {\,\frac{{dm}}{{dt}}\,} \right|= \mu$ . Its initial mass is $m_0$ and it is moving with velocity on a frictionless horizontal surface. The distance travelled by it till it melts completely is :
→The net applied force on a body in uniform circular motion should always be
A tank of height $5\, m$ is full of water. There is a hole of cross sectional area $1\, cm^2$ in its bottom. The initial volume of water that will come out from this hole per second is
→Modulus of rigidity of ideal liquids is