Question

Write two different vectors having the same direction.

Answer 1

Consider \(\overrightarrow p=(\hat i+\hat j+\hat k)\) and \(\overrightarrow q=(2\hat i+2\hat j+2\hat k)\).

The direction cosines of \(\overrightarrow p\) are given by,

\(I=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}\), \(m=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}\), and \(n=\frac{1}{\sqrt{1^2+1^2+1^2}}=\frac{1}{\sqrt 3}\).

The direction cosines of \(\overrightarrow q\) are given by

\(I=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}\), \(m=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}\), and \(n=\frac{2}{\sqrt{2^2+2^2+2^2}}=\frac{2}{2\sqrt3}\frac{1}{\sqrt 3}\).

The direction cosines of \(\overrightarrow p\) and \(\overrightarrow q\) are the same. Hence, the two vectors have the same direction.