Chapter 8 - Polar Coordinates; Vectors - Section 8.6 Vectors in Space - 8.6 Assess Your Understanding - Page 645: 27

$3i+4j-k$

If a vector $v$ initiates at point $A(x_1,y_1,z_1)$ and terminates at $B(x_2,y_2,z_2)$, then we can write the vector as $v =\lt x_2-x_1, y_2-y_1, z_2-z_1 \gt =(x_2-x_1)i+(y_2-y_1)j+(z_2-z_1)k.$ Here, we have: $A=(0,0,0)$ and $B=(3,4,-1)$ Therefore, $v=(3-0)i+(4-0)j+(-1-0)k\\ =3i+4j-k$