Write the Vector V in the Form Ai + Bj $$\| \mathbf { v } \| = 7 , \quad \alpha = 60 ^ { \circ }$$

question 124

Multiple Choice

Write the vector v in the form ai + bj, given its magnitude v and the angle  it makes with the positive x-axis.
- $$\| \mathbf { v } \| = 7 , \quad \alpha = 60 ^ { \circ }$$

• A) \(v = 7 \left( - \frac { 7 } { 2 } i - \frac { 7 \sqrt { 3 } } { 2 } j \right)\)
• B) \(v = 7 \left( \frac { 7 \sqrt { 3 } } { 2 } \mathrm { i } + \frac { 7 } { 2 } \mathrm { j } \right)\)
• C) \(v = 7 \left( \frac { \sqrt { 2 } } { 2 } \mathrm { i } + \frac { \sqrt { 2 } } { 2 } \mathrm { j } \right)\)
• D) \(v = 7 \left( \frac { 7 } { 2 } \mathrm { i } + \frac { 7 \sqrt { 3 } } { 2 } \mathrm { j } \right)\)

---

Definitions:

Authorized Act

An action that has been officially approved or sanctioned by the proper authority.

Express Authority

The clear, direct authority granted by a principal to an agent, specifically outlined in their agreement.

Actual Authority

An agent’s ability to affect the principal’s legal relations. Consent must be communicated to the agent.

Authorized Sale

A sale that is officially approved or permitted by the relevant authority or governing body, often following designated protocols or rules.