$A$ displacement vector has a $Y$-axis component of $10$ units. If it makes an angle of $30^{\circ}$ with the $X$-axis,find the magnitude of the vector.

Find the magnitude and direction of the vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$. What are the components of a vector $\vec{A}=2\hat{i}+3\hat{j}$ along the directions of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$?

For the given vector $\vec{A} = 3\hat{i} - 4\hat{j} + 10\hat{k}$,the ratio of the magnitude of its component on the $x-y$ plane to the component on the $z$-axis is:

One of the rectangular components of a force of $40 \ N$ is $20 \sqrt{3} \ N$. What is the other rectangular component (in $N$)?

The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis, the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).

Which one of the following pairs cannot be the rectangular components of a force vector of $10 \, N$?