Question
In a diamond exhibition, a diamond is covered in cubical glass box having coordinates O(0, 0, 0), A(1, 0, 0), B(1, 2, 0), C(0, 2, 0), O'(0, 0, 3), A'(1, 0, 3), B'(1, 2, 3) and C'(0, 2, 3). Based on the above information, answer the following questions.
  1. Direction ratios of OA are:
  1. < 0, 1, 0 >
  2. < 1, 0, 0 >
  3. < 0, 0, 1 >
  4. None of these
  1. Equation of diagonal OB' is:
  1. $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$
  2. $\frac{\text{x}}{0}=\frac{\text{y}}{1}=\frac{\text{z}}{2}$
  3. $\frac{\text{x}}{1}=\frac{\text{y}}{0}=\frac{\text{z}}{2}$
  4. None of these
  1. Equation of plane OABC is:
  1. x = 0
  2. y = 0
  3. z = 0
  4. None of these
  1. Equation of plane O' A' B' C' is:
  1. x = 3
  2. y = 3
  3. z = 3
  4. z = 2
  1. Equation of plane ABB' A' is:
  1. x = 1
  2. y = 1
  3. z = 2
  4. x = 3

Answer

  1. (b) < 1, 0, 0 >
​​​​​​​Solution:

D.R'. s of OA are < 1 - 0, 0 - 0, 0 - 0 >,

i.e., < 1, 0, 0 >
  1. (a) $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$
​​​​​​​​​​​​​​​​​​​​​Solution:

Equation of diagonal OB' is

$\frac{\text{x}-0}{1}=\frac{\text{y}-0}{2}=\frac{\text{z}-0}{3}$

i.e., $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$
  1. (c) z = 0
​​​​​​​​​​​​​​​​​​​​​​​​​​​​Solution:

OABC is xy-plane, therefore its equation is z = 0.
  1. (c) z = 3
​​​​​​​​​​​​​​​​​​​​​​​​​​​​Solution:

Plane O' A' B' C' is parallel to xy-plane passing through (0, 0, 3), therefore its equation is z = 3.
  1. (a) x = 1
​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Solution:

Plane ABB' A' is parallel to yz-plane passing through ( 1, 0, 0), therefore its equation is x = 1.

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