Consider the family of planes where is a parameter intersecting the coordinate axes…

MATHEMATICS · Single correct · ISC · Mathematics · Three-Dimensional Geometry · Three-Dimensional Geometry

Problem

Consider the family of planes

x + y + z = c

where

c

is a parameter intersecting the coordinate axes at

P, Q

and

R

and

\alpha, \beta

and

\gamma

are the angles made by each member of this family with positive

x, y

and

z

-axes. Which of the following interpretations hold good for this family? (1) Each member of this family is equally inclined with coordinate axes. (2)

\sin^2 \alpha + \sin^2 \beta + \sin^2 \gamma = 1

(3)

\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 2

(4) For

c = 3

area of the

\Delta PQR

3\sqrt{3}

sq units.