Chapter 5.1, Problem 14SSC

To determine

The resulting vector by subtracting vector K from vectorL .

Answer to Problem 14SSC

The resulting vector by subtracting vector K from vectorL is $10.0$.

Explanation of Solution

Given:

Two vectors K and Lare :

  

Figure 1

Formula used:

To find the difference of a given set of vectors,

(i) Each vector is resolved into its horizontal and vertical components

(ii) Respective components are added.

  $\begin{array}{l}{S}_x=K_x+L_x+M_x\\ S_y=K_y+L_y+M_y\end{array}$ ........ (1)

(iii)The magnitude of the algebraic sum vector is given by

  $S=\sqrt{S_x^2+S_y^2}$

(iv) The angle of the sum vector with horizontal axis is given by,

  $\theta ={\tan }^{-1}\left(\frac{S_y}{S_x}\right)$

Calculation:

Consider the two vectors given in Figure 1.

Here, the first vector isK . The vector is directed in the − x -direction. So it has only x -component and its value is given as,

  $K_x=-4.0$

The y -component of vector K is zero.

For vector L , only x-component exists and is given by,

  $L_x=6.0$

Subtracting a vector from another implies, adding the negated version of one vector to the other.

The entire process along with resultant vector is graphically expressed in Figure 2.

  

The resultant vector is,

  $\begin{array}{c}{S}_x=6.0-\left(-4.0\right)\\ =10.0\end{array}$

There will not be angular part since the difference vector is horizontal.

Conclusion :

Thus, the difference of the given vectors is 10.