Chapter 10: Q.24 (page 848)

Compute the lengths of the four diagonals of the parallelepiped
determined by \(u=i\), \(v=2j\), and \(w=2k\).

Short Answer

Expert verified

The lengths of the four diagonals are \(5,5,2\sqrt2,\text{ and }3\).

Step by step solution

Given Information

A parallelepiped formed by \(u=i\), \(v=2j\), and \(w=2k\).

There are four diagonals three faces and one body diagonal.

Three faces diagonals are:

\(d_1=u+v\)

\(d_2=u+w\)

\(d_3=v+w\)

One body diagonal is:

\(d_4=u+v+w\)

Calculate the lengths of the diagonals

The length of 1st face diagonal:

\(d_1=|i+2j|\)

\(d_1=\sqrt{1+4}\)

\(d_1=\sqrt5\)

The length of 2nd face diagonal:

\(d_2=|i+2k|\)

\(d_2=\sqrt{1+4}\)

\(d_2=\sqrt5\)

The length of 3rd face diagonal:

\(d_3=|2j+2k|\)

\(d_3=\sqrt{4+4}\)

\(d_3=2\sqrt2\)

The length of the body diagonal:

\(d_4=|i+2j+2k|\)

\(d_4=\sqrt{1+4+4}\)

\(d_4=3\)

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Compute the lengths of the four diagonals of the parallelepiped
determined by \(u=i\), \(v=2j\), and \(w=2k\).

Short Answer

Step by step solution

Given Information

Calculate the lengths of the diagonals

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Compute the lengths of the four diagonals of the parallelepipeddetermined by \(u=i\), \(v=2j\), and \(w=2k\).

Short Answer

Step by step solution

Given Information

Calculate the lengths of the diagonals

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Applied Mathematics

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Compute the lengths of the four diagonals of the parallelepiped
determined by \(u=i\), \(v=2j\), and \(w=2k\).