(d) The vectors perpendicular to … lie along a line

True or false, with reason or example:

(a) $|\mathbf{V}+\mathbf{W}{|}^2$ is never larger than $|\mathbf{V}{|}^2+|\mathbf{W}{|}^2$

(b) In a real triangle $|\mathbf{V}+\mathbf{W}|$ never equals $|\mathbf{V}|+|\mathbf{W}|$

(c) $\mathbf{V}\cdot \mathbf{W}$ equals $\mathbf{W}\cdot \mathbf{V}$

(d) The vectors perpendicular to $\mathbf{i}+\mathbf{j}+\mathbf{k}$ lie along a line.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.1 Vectors and Dot Products, #43