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If an AC current is given by $i = i_m \sin(\omega t)$, the instantaneous power dissipated in a resistor $R$ is given by:
The context states: 'The instantaneous power dissipated in the resistor is $p = i^2 R = i_m^2 R \sin^2 (\omega t)$'. This directly provides the formula for instantaneous power.
Which of the following physical quantities is defined as a vector product of two vectors?
According to the NCERT text, 'Two important quantities in the study of rotational motion, namely, moment of a force and angular momentum, are defined as vector products.'
If $\vec{a}$ and $\vec{b}$ are two vectors and $\theta$ is the angle between them, the magnitude of their vector product $\vec{c} = \vec{a} \times \vec{b}$ is given by:
The NCERT text states: '(i) magnitude of $c = c = ab \sin\theta$ where a and b are magnitudes of $\vec{a}$ and $\vec{b}$ and $\theta$ is the angle between the two vectors.'
The direction of the vector product $\vec{c} = \vec{a} \times \vec{b}$ is perpendicular to:
The NCERT text specifies: '(ii) $\vec{c}$ is perpendicular to the plane containing $\vec{a}$ and $\vec{b}$'.
Which rule is commonly used to determine the direction of the vector product of two vectors?
The NCERT text describes: '(iii) if we take a right handed screw... and if we turn the head in the direction from $\vec{a}$ to $\vec{b}$, then the tip of the screw advances in the direction of $\vec{c}$. This right handed screw rule is illustrated in Fig. 6.15a.' It also mentions the right-hand rule with curling fingers.
When determining the angle $\theta$ for the vector product $\vec{a} \times \vec{b}$, which range of angles should be considered?
The NCERT text states: 'While applying either of the above rules, the rotation should be taken through the smaller angle ($<180^\circ$) between $\vec{a}$ and $\vec{b}$'.
The vector product is also known as the:
The NCERT text explicitly states: 'Because of the cross ($\times$) used to denote the vector product, it is also referred to as cross product.'
Which of the following statements is TRUE regarding the vector product?
The NCERT text highlights: 'The vector product, however, is not commutative.' It further illustrates this with '$\vec{j} \times \vec{i} = -\vec{k}$' whereas '$\vec{i} \times \vec{j} = \vec{k}$'.
If $\vec{a} = 3\hat{i} + 4\hat{j} - 5\hat{k}$ and $\vec{b} = -2\hat{j} + 3\hat{k}$, what is the value of $\vec{a} \cdot \vec{b}$?
The scalar product (dot product) is calculated as $A_x B_x + A_y B_y + A_z B_z$. Given $\vec{a} = 3\hat{i} + 4\hat{j} - 5\hat{k}$ and $\vec{b} = 0\hat{i} - 2\hat{j} + 3\hat{k}$, then $\vec{a} \cdot \vec{b} = (3)(0) + (4)(-2) + (-5)(3) = 0 - 8 - 15 = -23$. This is based on Example 6.4 which asks for both scalar and vector product, but only shows the calculation for scalar product (dot product).
For unit vectors $\hat{i}$, $\hat{j}$, and $\hat{k}$, which of the following is correct?
The NCERT text lists the results: '(i) $\hat{i} \times \hat{i} = 0, \hat{j} \times \hat{j} = 0, \hat{k} \times \hat{k} = 0$' and '(ii) $\hat{i} \times \hat{j} = \hat{k}$, $\hat{j} \times \hat{k} = \hat{i}$, $\hat{k} \times \hat{i} = \hat{j}$.' Based on this, option o3 is correct.
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The bank mixes NEET previous year questions (PYQs) with practice questions, each tagged with its exam appearances where applicable.