Question

If , then what is $\left|-\frac{1}{2}\stackrel{\rightharpoonup }{v}\right|?$?

Short answer

The value of $\left|-\frac{1}{2}\stackrel{\rightharpoonup }{v}\right|$ is 3.08 m/s.

Step-by-step solution

Understanding the concept of multiplication of vector with a scalar

If a vector is multiplied by a scalar, its corresponding components get multiplied by the scalar individually.

The magnitude of a particular vector can be evaluated when its corresponding components are squared and added. Then its square root needs to be found.

Determination of the velocity vector  -12v⇀

The given velocity vector is _{.$\stackrel{\rightharpoonup }{v}=\left(2,-3,5\right)m/s$}

Multiply the given vector by $-\frac{1}{2}$ to get the required velocity vector,

Determination of magnitude of  -12v⇀

Take the square root of the sum of the squares of all the components of the vectors to obtain the required magnitude,

$$\begin{gathered} \left|-\frac{1}{2}\stackrel{\rightharpoonup }{v}\right|=\sqrt{{\left(-1\right)}^2\left(\frac{3}{2}\right){\left(-\frac{5}{2}\right)}^{2}m/s} \\ =\sqrt{1\pm \frac{9}{4}}\pm \frac{25}{4}m/s \\ \sqrt{\frac{4\pm 9\pm 25}{4}}m/s \\ =3.08m/s \end{gathered}$$