This item first appeared in Mathematics Magazine,
Vol 43 No. 4, September 1970, pp. 229-230.
Published by the Mathematical Association of America.
Problem 750. [January, 1970] Proposed by Charles W. Trigg, San Diego, California.Evaluate the determinant
||||a2 + b2 - c2 - d2||2bc - 2ad||2bd + 2ac||||
||||2bc + 2ad||a2 - b2 + c2 - d2||2cd - 2ab||||
||||2bd - 2ac||2cd + 2ab||a2 - b2 - c2 + d2||||
Solution by Nigel F. Nettheim, Bureau of the Census, Washington, D. C.The determinant equals the volume of the parallelepiped formed by the three vectors whose Cartesian coordinates are given by the rows of the matrix. The squared length of the first vector is