Show that the four points A(4,5,1), B(0,-1,-1), C(3,9,4) and D(-4,4,4)
are coplanar.

Let A= R × R and * be a binary operation on A defined by

(a, b) * (c, d) = (a+c, b+d)

Show that * is commutative and associative. Find the identity element for *

on A. Also find the inverse of every element (a, b) ∈ A.

Show that semi-vertical angle of a cone of maximum volume and given slant height is cos^-1.

15.

Using properties of determinants, prove that

Write the sum of intercepts cut off by the plane on the three axes.