Mathematics in Physics

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

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

$\vec{A}$ 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

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

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 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 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

For the vector $\vec{A}$ making an angle $\theta$ with the negative X-axis and lying in the third quadrant, the standard resolved form is

What is the relation between the two vectors $\vec{A} = 2\hat{i} + 5\hat{j} - 6\hat{k}$ and $\vec{B} = \hat{i} + \dfrac{5}{2}\hat{j} - 3\hat{k}$ ?

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

If $\vec{A} = \vec{B} + \vec{C}$ and magnitudes of $\vec{A}, \vec{B}$ and $\vec{C}$ are 5, 4 and 3 units respectively. The angle between $\vec{A}$ and $\vec{C}$ is

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