The components of vec a = 2hat i + 3hat | vedclass

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Question

The vector component of $\mathrm{A}$ in the direction of $\mathrm{B}$ is $A \cos 	heta=\frac{5}{\sqrt{2}}$

Vector $\mathrm{A}=2 \hat{i}+3 \hat{j}$

Vedclass · Accepted Answer

$\frac{5}{\sqrt{2}}\,\left( {\hat i + \hat j} \right)$

Vedclass · Answer

The vector component of $\mathrm{A}$ in the direction of $\mathrm{B}$ is $A \cos 	heta=\frac{5}{\sqrt{2}}$

Vector $\mathrm{A}=2 \hat{i}+3 \hat{j}$

Vector $\mathrm{B}=\hat{i}+\hat{j}$

We know that,

The vector component of $A$ in the direction of $B$ is

$\vec{A} \cdot \vec{B}=|A||B| \cos 	heta$

$A \cos 	heta=\frac{\vec{A} \cdot \vec{B}}{|B|}$

$A \cos 	heta=\frac{2 \hat{\imath}+3 \hat{\jmath} \cdot \hat{\imath}+\hat{\jmath}}{\sqrt{2}}$

$A \cos 	heta=\frac{5}{\sqrt{2}}$

Hence, The vector component of $A$ in the direction of $B$ is $A \cos 	heta=\frac{5}{\sqrt{2}}$

The components of $\vec a = 2\hat i + 3\hat j$ along the direction of vector $\left( {\hat i + \hat j} \right)$ is

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