Question

Match the following columns:

	Column I		Column II
(A)	The angle between any two diagonals of a cube is	(P)	cos-1(√(2/3))
(B)	The angle between one diagonal of a unit cube and a diagonal of a face is	(Q)	sin–1(1/3)
(C)	The angle between a diagonal of a cube and a diagonal of a face intersecting it	(R)	cot–1(1/√3)
(D)	The angle between the diagonal of the faces of the cube through the same vertex is	(S)  (T)	cot–1(√2) cos–1(1/3)

Answer 1

Answer is

(A) - (T)

(B) - (S)

(C) - (S)

(D) - (R)

(A) Let two diagonals of a cube are ai + aj + ak and – ai + aj + ak

Let θ be the angle between them

(B) Let the diagonal of the cube be i + j + k and the diagonal of the face be i + j.

Let θ be the angle between them,

(C) Let the diagonal of the cube be i + j + k and the diagonal of the face intersecting it is j + k.

Let θ be the angle between them,

(D) Let the diagonal of the faces of the same vertex are i + j, j + k.

Let θ be the angle between them. Then