Question

A vector $\overrightarrow{A}$ makes an angle of 20° and $\overrightarrow{B}$ makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3m and 4m respectively. Resultant is-

• A. 3 m
• B. 4 m
• C. 5 m
• D. 6 m

Answer 1

Answer: (C)

5 m

Answer 2

Given vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ with magnitudes $A=3$ m and $B=4$ m, making angles $20^\circ$ and $110^\circ$ with the X-axis, respectively. The angle between the vectors is $\theta = 110^\circ - 20^\circ = 90^\circ$. The magnitude of the resultant vector $R$ is calculated using the formula: $R = \sqrt{A^2 + B^2 + 2AB \cos\theta}$ Substituting the given values: $R = \sqrt{3^2 + 4^2 + 2(3)(4)\cos(90^\circ)}$ $R = \sqrt{9 + 16 + 24(0)}$ $R = \sqrt{25}$ $R = 5$ m.