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Direction Cosines and Direction Ratios — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDirection Cosines and Direction Ratios1 Mark
Question
A parallelopiped is formed by planes drawn through the point (2, 3, 5) and (5, 9, 7) parallel to the coordinate planes. The length of a diagonal of the parallelopiped is:
  1. $7$
  2. $\sqrt{38}$
  3. $\sqrt{155}$
  4. $\text{none of these}$
✓

Answer

  1. 7

Solution:

The given point (2, 3, 5) and (5, 9, 7) are two diagonally opposite vertices of the parallelopiped as all of theire coordinates are different.

$\therefore$ Edges of the paralleloppiped

= |2 - 5|, |3 - 9| and |5 - 7|

=3, 6 and 2.

Now,

Length of the diagonal of the parallelopiped

$=\sqrt{3^2+6^2+2^2}$

$=\sqrt{9+36+4}$

$=\sqrt{49}$

$=7$

Hence, length of the diagonal of the parallelepiped formed by the planes

Parallel to coordinate planes and drawn through point (2, 3, 5)and (5, 9, 7) is 7 units.

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