If overrightarrow{A} is a vector with magnitu | vedclass

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

Question

(N/A) The vector is given as $\overrightarrow{A} = 3\hat{i} + 4\hat{j}$.The magnitude of $\overrightarrow{A}$ is $|\overrightarrow{A}| = \sqrt{3^2 + 4

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) The vector is given as $\overrightarrow{A} = 3\hat{i} + 4\hat{j}$.
The magnitude of $\overrightarrow{A}$ is $|\overrightarrow{A}| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.
The unit vector $\hat{A}$ is defined as $\hat{A} = \frac{\overrightarrow{A}}{|\overrightarrow{A}|} = \frac{3\hat{i} + 4\hat{j}}{5} = \frac{3}{5}\hat{i} + \frac{4}{5}\hat{j}$.
The magnitude of the unit vector is $|\hat{A}| = \sqrt{(\frac{3}{5})^2 + (\frac{4}{5})^2} = \sqrt{\frac{9}{25} + \frac{16}{25}} = \sqrt{\frac{25}{25}} = \sqrt{1} = 1$.
Thus,the magnitude of the unit vector is $1$.

If $\overrightarrow{A}$ is a vector with magnitude $(3, 4)$,show that the magnitude of its unit vector is $1$.

Similar Questions

$A$ vector is added to an equal and opposite vector of similar nature,it forms a ........

The condition $( a \cdot b )^2 = a^2 b^2$ is satisfied when

If $\vec{A}$ and $\vec{B}$ are two non-zero vectors such that $|\vec{A} + \vec{B}| = \frac{|\vec{A} - \vec{B}|}{2}$ and $|\vec{A}| = 2|\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is

Find the length of the component of $\vec{a}$ along $\vec{b}$,where $\vec{a} = 4 \hat{i} + 5 \hat{j}$ and $\vec{b} = -\hat{i} + \hat{j}$.

The values of $x$ and $y$ for which vectors $\vec{A} = (6 \hat{i} + x \hat{j} - 2 \hat{k})$ and $\vec{B} = (5 \hat{i} + 6 \hat{j} - y \hat{k})$ are parallel are

Vedclass Test Series

Exam Paper Generator

Online Exam Module