Vectors vec{A} and vec{B} make angles of 20^c | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The angle between vectors $\vec{A}$ and $\vec{B}$ is $	heta = 110^\circ - 20^\circ = 90^\circ$.The magnitude of the resultant vector $\vec{R}$ is

Vedclass · Accepted Answer

$	an^{-1}(12/5)$

Vedclass · Answer

(B) The angle between vectors $\vec{A}$ and $\vec{B}$ is $	heta = 110^\circ - 20^\circ = 90^\circ$.The magnitude of the resultant vector $\vec{R}$ is given by:$R = \sqrt{A^2 + B^2 + 2AB \cos 90^\circ} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \, m$.Let $\alpha$ be the angle that the resultant vector $\vec{R}$ makes with vector $\vec{A}$.Using the formula $	an \alpha = \frac{B \sin 	heta}{A + B \cos 	heta}$:$	an \alpha = \frac{12 \sin 90^\circ}{5 + 12 \cos 90^\circ} = \frac{12 	imes 1}{5 + 12 	imes 0} = \frac{12}{5}$.Thus,$\alpha = 	an^{-1}(12/5)$.Since $\vec{A}$ makes an angle of $20^\circ$ with the $X$-axis,the angle of the resultant vector $\vec{R}$ with the $X$-axis is $\alpha + 20^\circ = 	an^{-1}(12/5) + 20^\circ$.

Vectors $\vec{A}$ and $\vec{B}$ make angles of $20^\circ$ and $110^\circ$ with the $X$-axis respectively. The magnitudes of these vectors are $5 \, m$ and $12 \, m$ respectively. Find the angle made by the resultant vector with the $X$-axis.

Similar Questions

Find the resultant of three vectors $\overrightarrow{OA}$,$\overrightarrow{OB}$,and $\overrightarrow{OC}$ as shown in the figure. The radius of the circle is $R$.

Write two properties of vector addition.

If the square of the resultant of two forces of equal magnitude is equal to three times their product,then the angle between them is ........ $^o$.

If the magnitude of the resultant of two vectors of equal magnitude is equal to the magnitude of either vector,then find the angle between the two vectors. (in $^{\circ}$)

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces

Vedclass Test Series

Exam Paper Generator

Online Exam Module