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What characteristic makes many halogenated compounds persist in the environment?
The text states: 'Halogenated compounds persist in the environment due to their resistance to breakdown by soil bacteria.'
Which of the following statements about unit vectors is INCORRECT?
According to the NCERT text, '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.' Therefore, the statement that unit vectors have specific dimensions and units is incorrect.
A vector $\vec{A}$ lies in the x-y plane. If its x-component is $A_x$ and its y-component is $A_y$, how can $\vec{A}$ be expressed in terms of unit vectors $\hat{i}$ and $\hat{j}$?
The NCERT text states, 'Thus, $\vec{A} = A_x \hat{i} + A_y \hat{j}$.' This equation correctly represents a vector in terms of its components along the x and y axes using unit vectors.
If a vector $\vec{A}$ has a magnitude $|A|$ and a unit vector along its direction is $\hat{n}$, which of the following expressions is correct?
According to equation 3.10 in the NCERT text, 'In general, a vector A can be written as $\vec{A} = |A| \hat{n}$ where $\hat{n}$ is a unit vector along A.'
Which of the following is NOT a characteristic of a unit vector?
A unit vector is used to specify direction. Multiplying a unit vector by a scalar changes its magnitude, not its direction (unless the scalar is negative, which reverses the direction). The NCERT states: 'If we multiply a unit vector, say $\hat{n}$ by a scalar $\lambda$, the result is a vector $\lambda \vec{n}$.'
A vector $\vec{A}$ is resolved into two component vectors, $\vec{A_1}$ and $\vec{A_2}$. If $\vec{A_1}$ is parallel to $\hat{i}$ and $\vec{A_2}$ is parallel to $\hat{j}$, which condition must be met for this resolution?
The NCERT text explicitly states: 'We draw lines from the head of A perpendicular to the coordinate axes as in Fig. 3.9(b), and get vectors $\vec{A_1}$ and $\vec{A_2}$ such that $\vec{A_1} + \vec{A_2} = \vec{A}$'.
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.'
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