Question

A vector is represented by 3\[\hat i\] + \[\hat j\] + 2\[\hat k\]. Its length in XY plane is ______.

Options

• 2

• \[\sqrt 14\]

• \[\sqrt 10\]

• \[\sqrt 5\]

Answer 1

A vector is represented by 3\[\hat i\] + \[\hat j\] + 2\[\hat k\]. Its length in XY plane is \[\sqrt 10\].

Explanation:

\[\vec R\] = 3\[\hat i\] + \[\hat j\] + 2\[\hat k\]

\[\therefore\] Length in XY plane = \[\sqrt{\mathrm{R}_{x}^{2}+\mathrm{R}_{y}^{2}}=\sqrt{3^{2}+1^{2}}\]

= \[\sqrt {10}\]