The component of vector vec A = 2hat i + | vedclass

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

Question

Let $\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$
Component

Vedclass · Accepted Answer

$\frac{5}{{\sqrt 2 }}$

Vedclass · Answer

Let $\overrightarrow{\mathrm{A}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}$ and $\overrightarrow{\mathrm{B}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$
Component of $\vec{\mathrm{A}}$ in direction of $\overrightarrow{\mathrm{B}}=\frac{(\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}) \overrightarrow{\mathrm{B}}}{\mathrm{B}^{2}}$
$=\frac{(2 	imes 1+3 	imes 1)(\hat{i}+\hat{j})}{2}=\frac{5}{2}(\hat{i}+\hat{j})$
Magnitude of component $=\frac{5}{\sqrt{2}}$

The component of vector $\vec A = 2\hat i + 3\hat j$ along the vector $\hat i + \hat j$ is

Similar Questions

What is the maximum number of rectangular components into which a vector can be split in space?

Consider a vector $F =4 \hat{ i }-3 \hat{ j }$. Another vector perpendicular of $F$ is

The resultant of $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$, then

If the angle between two vectors $A$ and $B$ is $120^{\circ}$, its resultant $C$ will be

A vector $\overrightarrow a $ is turned without a change in its length through a small angle $d\theta .$The value of $|\Delta \overrightarrow a |$ and $\Delta a$ are respectively