Find a vector in the direction of vector $\vec{a}=3\hat{i}-4\hat{j}$ that has a magnitude of $10$ units.

Given vector $\vec{a}=3\hat{i}-4\hat{j}$.The magnitude of $\vec{a}$ is:
$$|\vec{a}|=\sqrt{3^2+(-4{)}^2}=\sqrt{9+16}=5$$
The unit vector in the direction of $\vec{a}$ is:
$$\hat{a}=\frac{\vec{a}}{|\vec{a}|}=\frac{3\hat{i}-4\hat{j}}{5}$$
A vector with magnitude $10$ in the direction of $\vec{a}$ is:
$$\vec{v}=10\hat{a}=10\left(\frac{3\hat{i}-4\hat{j}}{5}\right)$$
$$\vec{v}=2(3\hat{i}-4\hat{j})=6\hat{i}-8\hat{j}$$