Q.Find the distance from $(4,-2,6)$ to the Z-axis.

Locating a point in space needs three mutually perpendicular axes OX, OY, OZ through an origin O, with the positive Z-direction fixed by the right-hand rule; a point is then an ordered triple (x, y, z), and this triple gives its (signed) distances from the three coordinate planes: |z| from the XY-plane, |x| from the YZ-plane, |y| from the XZ-plane. The unit vectors along the positive X, Y, Z axes are named i, j, k, and every vector in space can be written uniquely as a1 i + a2 j + a3 k, where a1, a2, a3 are called its components; its magnitude is then sqrt(a1^2+a2^2+a3^2). Space is divided by the three coordinate planes into eigh …