Answer
Magnitude: $25$
Direction angle: $106.26^{\circ}$
Work Step by Step
The magnitude $|u|$ of vector $u=\left\langle a,b\right\rangle$ is given by $|u|=\sqrt {a^2+b^2}$.
For the given vector
$u=\left\langle -7,24\right\rangle \Rightarrow ~ a=-7, b=24.$
Therefore,
$|u|=|\left\langle -7,24\right\rangle|=\sqrt {(-7)^2+(24)^2}=\sqrt {49+576}=\sqrt {625}=25$
Hence the magnitude of the vector $\left\langle -7,24\right\rangle$ is $25$.
The direction angle $\theta$ of vector $u=\left\langle a,b\right\rangle$ is given by
$\theta=\tan^{-1}\left(\frac{b}{a}\right)$
Therefore, for $u=\left\langle -7,24\right\rangle $ we have
$\theta=\tan^{-1}\left(\frac{24}{-7}\right)=106.26^{\circ}$
Hence, the magnitude of $\left\langle -7,24\right\rangle$ is $25$ and the direction angle is $106.26^{\circ}$
