MCQ
Figure shows the orientation of two vectors $u$ and $v$ in the $XY$ plane.

If $\text{u}=\text{a}\hat{\text{i}}+\text{b}\hat{\text{j}}$ and $\text{v}=\text{p}\hat{\text{i}}+\text{q}\hat{\text{j}}$ which of the following is correct?
  • A
    $a$ and $p$ are positive while $b$ and $q$ are negative.
  • $a, p$ and $b$ are positive while $q$ is negative.
  • C
    $a, q$ and $b$ are positive while $p$ is negative.
  • D
    $a, b, p$ and $q$ are all positive.

Answer

Correct option: B.
$a, p$ and $b$ are positive while $q$ is negative.
Main concept used: Sign of $a, b, p$ and $q$ are the sign of their resolving components in the $XY$ direction.
Explanation: Components along $X$ and $Y$ axis of the vector $\vec{\text{u}}$ are both $+X$ and $Y$ direction,
so $a, b$ are positive.
Now if we resolve

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

In the following problems, indicate the correct direction of friction force acting on the cylinder, which is pulled on a rough surface by a constant force $F$. $A$ spool is pulled vertically by a constant force $F ( < Mg)$ as shown in figure The friction force canbe given by which of the following diagrams
A body of mass $M$ tied to a string is lowered at a constant acceleration of $(g/4)$ through a vertical distance $h$. The work done by the string will be..............
The efficiency of carnot engine is $50\%$ and temperature of sink is $500\,K$ . If temperature of source is kept constant and its efficiency raised to $60\%$ , then the required temperature of the sink will be  .... $K$
Select the incorrect relation. (Where symbols have their usual meanings)
When no current is passed through a conductor:
  1. The free electrons do not move.
  2. The average speed of a free electron over a large period of time is zero.
  3. The average velocity of a free electron over a large period of time is zero.
  4. The average of the velocities of all the free electrons at an instant is zero.
Match List $I$ with List $II$.

  List $I$   List $II$
$(A)$ Torque $(I)$ $Nms^{-1}$
$(B)$ Stress $(II)$ $J\,kg^{-1}$
$(C)$ Latent Heat $(III)$ $Nm$
$(D)$ Power $(IV)$ $Nm^{-2}$

Choose the correct answer from the options below.

A projectile projected at an angle ${30^o}$ from the horizontal has a range $2\upsilon ,\,\sqrt 2 \upsilon \,\,{\rm{ and}}\,{\rm{zero}}$. If the angle of projection at the same initial velocity be ${60^o}$, then the range will be
A swimmer can swim with speed '$v$' with respect to still water in a river which is flowing with speed $u$. There is a float moving with the river. Now the swimmer overtakes float and gets a lead of $l$ and returns back to the float. Time taken by swimmer in this process will be
A body of mass $m$ kg. starts falling from a point $2R$ above the Earth’s surface. Its kinetic energy when it has fallen to a point $‘R’$ above the Earth’s surface [$R-$Radius of Earth, $M-$Mass of Earth, $G-$Gravitational Constant]
‘Gulab Jamuns’ $($assumed to be spherical$)$ are to be heated in an oven. They are available in two sizes, one twice bigger $($in radius$)$ than the other. Pizzas $($assumed to be discs$)$ are also to be heated in oven. They are also in two sizes, one twice big $($in radius$)$ than the other. All four are put together to be heated to oven temperature. Choose the correct option from the following: