The rules for combining scalar quantities are the rules of:
As per the NCERT text, 'The rules for combining scalars are the rules of ordinary algebra. Scalars can be added, subtracted, multiplied and divided'.
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The rules for combining scalar quantities are the rules of:
As per the NCERT text, 'The rules for combining scalars are the rules of ordinary algebra. Scalars can be added, subtracted, multiplied and divided'.
A unit vector is characterized by:
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.'
What happens when a vector $\vec{A}$ is multiplied by a positive real number $\lambda$?
As per the NCERT, 'Multiplying a vector A with a positive number $\lambda$ gives a vector whose magnitude is changed by the factor $\lambda$ but the direction is the same as that of A : $|\lambda A| = \lambda |A|$ if $\lambda > 0$.'
If a vector $\vec{A}$ is multiplied by a negative number $-\lambda$, the new vector will have:
The NCERT text explains, 'Multiplying a vector A by a negative number $-\lambda$ gives another vector whose direction is opposite to the direction of A and whose magnitude is $\lambda$ times $|A|$'.
Which of the following is NOT an example of a scalar quantity?
The summary explicitly states, 'Scalar quantities are quantities with magnitudes only. Examples are distance, speed, mass and temperature.' It further states, 'Vector quantities are quantities with magnitude and direction both. Examples are displacement, velocity and acceleration.'
Unit vectors like $\hat{i}$, $\hat{j}$, and $\hat{k}$ are ___________ to each other in a rectangular coordinate system.
The text mentions, 'These unit vectors are perpendicular to each other.'
A vector $\vec{A}$ lying in the x-y plane can be resolved into its components as $\vec{A} = A_x \hat{i} + A_y \hat{j}$. What do $A_x$ and $A_y$ represent?
The NCERT states, 'The quantities $A_x$ and $A_y$ are called x-, and y- components of the vector'.
Which of the following properties is true for vector addition?
The summary lists: 'Vector addition is commutative : $\vec{A} + \vec{B} = \vec{B} + \vec{A}$' and 'It also obeys the associative law : $(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C})$'.
A null or zero vector has:
The summary defines: 'A null or zero vector is a vector with zero magnitude. Since the magnitude is zero, we don’t have to specify its direction.'
The subtraction of vector $\vec{B}$ from vector $\vec{A}$ is defined as:
The summary clearly states: 'The subtraction of vector B from A is defined as the sum of A and – B : $\vec{A} – \vec{B} = \vec{A} + (– \vec{B})$'.
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