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Consider a vector $\vec{A}$ making an angle $\theta$ with the x-axis. If $A_x$ is its x-component and $A_y$ is its y-component, which of the following relations is correct?
From the summary section, point 10 states: 'If vector A makes an angle $\theta$ with the x-axis, then $A_x = A \cos \theta$, $A_y = A \sin \theta$'.
What is the magnitude of a vector $\vec{A} = A_x \hat{i} + A_y \hat{j}$?
According to point 10 in the summary, the magnitude of a vector $\vec{A} = A_x \hat{i} + A_y \hat{j}$ is $|A| = \sqrt{A_x^2 + A_y^2}$.
If $\vec{r} = x \hat{i} + y \hat{j}$ is the position vector of an object in the x-y plane, what do $x$ and $y$ represent?
As stated in section 3.7.1, for a position vector $\vec{r} = x \hat{i} + y \hat{j}$, '$x$ and $y$ are components of $\vec{r}$ along x-, and y- axes or simply they are the coordinates of the object.'
A vector $\vec{A}$ can be resolved into components along two given vectors $\vec{a}$ and $\vec{b}$ lying in the same plane. This representation is given by:
Point 8 in the summary states: 'A vector A can be resolved into component along two given vectors a and b lying in the same plane: $\vec{A} = \lambda \vec{a} + \mu \vec{b}$ where $\lambda$ and $\mu$ are real numbers.'
What is the primary purpose of unit vectors in a rectangular coordinate system?
The NCERT states, 'A unit vector is a vector of unit magnitude and points in a particular direction. It has no dimension and unit. It is used to specify a direction only.' In a rectangular coordinate system, $\hat{i}$, $\hat{j}$, and $\hat{k}$ specifically point along the x-, y-, and z-axes, respectively, to specify direction.
If the x-component ($A_x$) and y-component ($A_y$) of a vector $\vec{A}$ are known, which expression correctly gives the angle $\theta$ that $\vec{A}$ makes with the x-axis?
From the summary section, point 10, it is given that '$\tan \theta = \frac{A_y}{A_x}$'.
Consider a vector $\vec{A}$. If $\vec{A_1}$ and $\vec{A_2}$ are its component vectors along the x and y axes respectively, then the component vectors are given by:
The NCERT text states: 'Since $\vec{A_1}$ is parallel to $\hat{i}$ and $\vec{A_2}$ is parallel to $\hat{j}$, we have : $\vec{A_1} = A_x \hat{i}$, $\vec{A_2} = A_y \hat{j}$ where $A_x$ and $A_y$ are real numbers.'
Which of the following physical properties is commonly used as the basis for constructing liquid-in-glass thermometers?
According to the NCERT text, 'The commonly used property is variation of the volume of a liquid with temperature. For example, in common liquid–in–glass thermometers, mercury, alcohol etc., are used whose volume varies linearly with temperature over a wide range.'
For defining a standard temperature scale, how many fixed reference points are typically needed?
The NCERT text states, 'For the definition of any standard scale, two fixed reference points are needed.'
What are the two convenient fixed points used for calibrating temperature scales related to water?
The context mentions, 'The ice point and the steam point of water are two convenient fixed points and are known as the freezing and boiling points, respectively.'
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.