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Chapter 10: Q.19 (page 848)

Compute the lengths of the diagonals of the parallelogram determined by \(u=i\) and \(v=2j\).

Short Answer

Expert verified

The lengths of diagonals are \(\sqrt5\) and \(\sqrt5\).

Step by step solution

01

Given Information

The sides of a parallelogram are \(u=i\) and \(v=2j\).

The lengths of the diagonal of a parallelogram \(u+v\) and \(u-v\).

02

Find the diagonal vector of the parallelogram

First diagonal \((u+v)=i+2j\).

Second diagonal \((u-v)=i-2j\).

03

Find the length of the diagonals

The length of the first diagonal:

\(=\sqrt{1^2+2^2}\)

\(=\sqrt{5}\).

The length of the second diagonal:

\(=\sqrt{1^2+(-2)^2}\)

\(=\sqrt{5}\).

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