question_answer

Is \[\text{\hat{i}}+\text{\hat{j}}\] a unit vector? Explain.                

Answer:

\[\text{(\hat{i}}+\text{\hat{j})}\]is not a unit vector. If \[\vec{R}=\text{\hat{i}}+\text{\hat{j}}\], then = \[\text{R }=\sqrt{{{(1)}^{2}}+{{(1)}^{2}}}=\sqrt{2}\] and angle \[\beta \] which \[\vec{R}\] make with X-axis is given by, \[\text{cos}\beta =1/\sqrt{2}~=\text{cos 45}{}^\circ \]or\[\theta =\text{45}{}^\circ \].