Question

(a) What is the vector whose tail is at $<9.5,7,0>$m and whose head is at $<4,-13,0>$m? (b) What is the magnitude of this vector?

Short answer

(a) The required vector is m.

(b) The magnitude of this vector is $\left|\overrightarrow{\alpha }\right|=20.74$m.

Step-by-step solution

Identification of given data

The given vector is,

Tail- m

Head- m

Calculating vector

To find the vector (denoted with ) which is between these two points, subtract the point that the tail on it from the point that the head on it(similar to finding displacement between two points).

Therefore, the required vector is m.

Calculating magnitude

(b) The magnitude of this vector (which we found in part (a) of this problem to be m) can becalculated as:

$$\begin{gathered} \left|\overrightarrow{\alpha }\right|=\sqrt{\left({\left(-5.5\right)}^2+{\left(-20\right)}^2\right)} \\ =20.74m \end{gathered}$$

Thus, the magnitude of the vector is $\left|\overrightarrow{\alpha }\right|=20.74m$m.