The unit vector parallel to the resultant of | vedclass

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

Question

(B) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$:$\vec{R} = \vec{A} + \vec{B} = (4\hat{i} - 3\hat{j}) + (8\ha

Vedclass · Accepted Answer

$\frac{12\hat{i} + 5\hat{j}}{13}$

Vedclass · Answer

(B) The resultant vector $\vec{R}$ is given by the sum of vectors $\vec{A}$ and $\vec{B}$:$\vec{R} = \vec{A} + \vec{B} = (4\hat{i} - 3\hat{j}) + (8\hat{i} + 8\hat{j})$$\vec{R} = (4 + 8)\hat{i} + (-3 + 8)\hat{j} = 12\hat{i} + 5\hat{j}$The magnitude of the resultant vector is:$|\vec{R}| = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13$The unit vector $\hat{R}$ parallel to the resultant is given by:$\hat{R} = \frac{\vec{R}}{|\vec{R}|} = \frac{12\hat{i} + 5\hat{j}}{13}$

The unit vector parallel to the resultant of vectors $\vec{A} = 4\hat{i} - 3\hat{j}$ and $\vec{B} = 8\hat{i} + 8\hat{j}$ is:

Similar Questions

The sum of the magnitudes of two forces acting at a point is $16 \,N$. If their resultant is normal to the smaller force and has a magnitude of $8 \,N$, then the forces are:

Two vectors $\vec A$ and $\vec B$ have magnitudes $2$ and $1$ respectively. If the angle between $\vec A$ and $\vec B$ is $60^{\circ}$,then which of the following vectors may be equal to $\frac{\vec A}{2} - \vec B$?

Three vectors each of magnitude $3 \sqrt{1.5}$ units are acting at a point. If the angle between any two vectors is $\frac{\pi}{3}$,then the magnitude of the resultant vector of the three vectors is

If $P + Q = R$ and $|P| = |Q| = \sqrt{3}$ and $|R| = 3$,then the angle between $P$ and $Q$ is

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $n$ times the magnitude of $(\vec A - \vec B)$. The angle between $\vec A$ and $\vec B$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module