Express the vector as a product of its length and direction.
-$- 3 i - \frac { 5 } { 4 } j$
A) $\frac { 13 } { 4 } ( - \mathbf { i } - \mathbf { j } )$
B) $\frac { 13 } { 4 } \left( - 3 i - \frac { 5 } { 4 } j \right)$
C) $\frac { 13 } { 4 } \left( - \frac { 12 } { 13 } \mathbf { i } - \frac { 5 } { 13 } \mathbf { j } \right)$
D) $\frac { 169 } { 16 } \left( - 3 \mathrm { i } - \frac { 5 } { 4 } \mathrm { j } \right)$

Question

Quizplus · Accepted Answer

To express the vector as a product of its length and direction, we first need to find the length (magnitude) of the vector. Using the Pythagorean theorem, we get:
$$\left|-3i - \frac{5}{4} jight| = \sqrt{(-3)^2 + \left(\frac{5}{4}ight)^2} = \frac{13}{4}$$
Next, we need to find the unit vector in the direction of the given vector. To do this, we divide the vector by its length:
$$\frac{-3i - \frac{5}{4}j}{\frac{13}{4}} = -\frac{12}{13}i - \frac{5}{13}j$$
Therefore, the vector can be expressed as the product of its length and direction as:
$$\frac{13}{4}\left(-\frac{12}{13}i - \frac{5}{13}jight) = \frac{13}{4}\left(-\frac{12}{13}iight) + \frac{13}{4}\left(-\frac{5}{13}jight) = \boxed{	extbf{(C)}}$$

Express the Vector as a Product of Its Length and Direction