Preeti started her own cooking channel on Youtube ‘Mood Art’. As her subscribers increased, she was not in a position to manage everything on her own. She hired Rahul and Riya to help her with filming, editing, lighting and content research. She granted authority to them to operate within prescribed limits. She was thus, able to use her time on high priority activities like developing new recipes and content development etc. As a result, Rahul and Riya were given opportunities to develop and exercise initiative. Preeti was now able to focus on objectives and meet the target of achieving a subscriber base of one million in six months.
(a) Identify and explain the function of management discussed in the above para.
(b) Explain any four points of importance of the function identified in (a).
Three friends A, B, and C move out from the same location O at the same time in three different directions to reach their destinations. They move out on straight paths and decide that A and B after reaching their destinations will meet up with C at his pre-decided destination, following straight paths from A to C and B to C in such a way that \( \overrightarrow{OA} = \hat{i}, \overrightarrow{OB} = \hat{j} \), and \( \overrightarrow{OC} = 5 \hat{i} - 2 \hat{j} \), respectively.
Based upon the above information, answer the following questions:
(i) Complete the given figure to explain their entire movement plan along the respective vectors.}
(ii) Find vectors \( \overrightarrow{AC} \) and \( \overrightarrow{BC} \).}
(iii) (a) If \( \overrightarrow{a} = 2 \hat{i} - \hat{j} + 4 \hat{k} \), distance of O to A is 1 km, and from O to B is 2 km, then find the angle between \( \overrightarrow{OA} \) and \( \overrightarrow{OB} \). Also, find \( | \overrightarrow{a} \times \overrightarrow{b} | \).}
(iii) (b) If \( \overrightarrow{a} = 2 \hat{i} - \hat{j} + 4 \hat{k} \), find a unit vector perpendicular to \( (\overrightarrow{a} + \overrightarrow{b}) \) and \( (\overrightarrow{a} - \overrightarrow{b}) \).