Mathematics in Physics

The area of a triangle formed by vectors $\vec{P} = (3\hat{i} - 4\hat{j} + 2\hat{k})$ m and $\vec{Q} = (\hat{i} + \hat{j} - 2\hat{k})$ m as adjacent sides is approximately

$\vec{A}$ and $\vec{B}$ are expressed as $\vec{A}=2\hat{i}+\hat{j}$ and $\vec{B}=\hat{i}-\hat{j}$. Unit vector perpendicular to $\vec{A}$ and $\vec{B}$ is

Out of the following vectors, identify the one which is normal to the force, $\vec{F} = 4\hat{i} - 3\hat{j}$.

The physical quantity $P=\dfrac{a^{3}b^{2}}{c^{1/3}d^{1/4}}$, where the percentage error in a, b, c, and d are $1\%$, $\dfrac{3}{2}\%$, $3\%$, and $2\%$ respectively. Then the percentage error in P is

A vector $\vec{B}$ is along positive y-axis and its vector product with another vector $\vec{A}$ is zero; then vector $\vec{A}$ could be

The initial velocity of an object is $\vec{u}=3\hat{i}+2\hat{j}$ m/s. Its constant acceleration is $\vec{a}=5\hat{i}+3\hat{j}$ m/s$^2$. The magnitude of the final velocity after $5$ s is

The metre scale is used to measure the volume of a block. The measured length is $10$ cm, breadth is $20$ cm and height is $25$ cm. The percentage error in the measurement of volume of a block $is\ldots$ (least count of…

The error in measurement of radius of sphere is $0.2\ \%$, then the percentage error in its volume is

The heat generated in a circuit is given by $Q = I^2 R t$. If the percentage error in the measurement of $Q$ is $1\%$, $R$ is $2\%$, and $t$ is $1\%$, then the percentage error in the measurement of current $I$ is

A body travels uniformly a distance of $(20 \pm 0.2)$ m in a time $(4.0 \pm 0.4)$ s. The percentage error in the value of velocity is

The least count of voltmeter is 0.2 V, and least count of ammeter is 1 mA. If the potential difference is 2 V, and the current is 10 mA, what is the percentage error in measurement of resistance?

Given $\vec{A} = 2\hat{i} - 2\hat{j} + 8\hat{k}$ and $\vec{B} = 2\hat{i} - m\hat{j} + 8\hat{k}$, if $\vec{A}$ and $\vec{B}$ have the same direction, the value of $m$ is