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# A Parallelopiped is Formed by Planes Drawn Through the Points (2, 3, 5) and (5, 9, 7), Parallel to the Coordinate Planes. the Length of Diagonal of the Parallelopiped is (A) 7 Sqrt(38) Sqrt(155) - CBSE (Arts) Class 12 - Mathematics

ConceptDirection Cosines and Direction Ratios of a Line

#### Question

A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7), parallel to the coordinate planes. The length of a diagonal of the parallelopiped is

• 7

• sqrt(38)

• sqrt(155)

• none of these

#### Solution

7

$\text{ The given points } \left( 2, 3, 5 \right) \text{ and } \left( 5, 9, 7 \right) \text{ are two diagonally opposite vertices of the parallelopiped as all of their coordinates are different }.$

$\therefore \text{ Edges of the parallelopiped } = \left| 2 - 5 \right|, \left| 3 - 9 \right| \text{ and } \left| 5 - 7 \right|$

$= 3, 6 \text{ and } 2$

$\text { Now} ,$

$\text{ Length of the diagonal of the parallelopiped } = \sqrt{\left( 3 \right)^2 + \left( 6 \right)^2 + \left( 2 \right)^2}$

$\hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} = \sqrt{9 + 36 + 4}$

$\hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} = \sqrt{49}$

$\hspace{0.167em} \hspace{0.167em} \hspace{0.167em} \hspace{0.167em} = 7$

$\text{ Hence, length of the diagonal of the parallelopiped formed by the planes parallel to coordinate planes and drawn through points } \left( 2, 3, 5 \right) \text { and } \left( 5, 9, 7 \right) \text{ is 7 units } .$

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Solution A Parallelopiped is Formed by Planes Drawn Through the Points (2, 3, 5) and (5, 9, 7), Parallel to the Coordinate Planes. the Length of Diagonal of the Parallelopiped is (A) 7 Sqrt(38) Sqrt(155) Concept: Direction Cosines and Direction Ratios of a Line.
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