Question 30: Motion in 2D & Vectors

Question

If $$\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m}$$ and $$\vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}$$. The magnitude of component of vector $$\vec{A}$$ along vector $$\vec{B}$$ will be ____________ $$\mathrm{m}$$.

Accepted Answer

$$
\begin{aligned}
& \vec{A} \cdot \vec{B}=(2 \hat{i}+3 \hat{j}-\hat{k}) \cdot(\hat{i}+2 \hat{j}+2 \hat{k}) \\
& \Rightarrow \vec{A} \cdot \vec{B}=2 	imes 1+3 	imes 2-1 	imes 2 \\
& \Rightarrow \vec{A} \cdot \vec{B}=6
\end{aligned}
$$
And $$
|\vec{B}|=\sqrt{1^2+2^2+2^2}=\sqrt{9}=3
$$
Magnitude of component of
$\vec{A}$ along $\vec{B}=\frac{\vec{A} \cdot \vec{B}}{|B|}=\frac{6}{3}=2$

Motion in 2D & Vectors

If $\vec{A}=(2 \hat{i}+3 \hat{j}-\hat{k})\, \mathrm{m} and \vec{B}=(\hat{i}+2 \hat{j}+2 \hat{k}) \,\mathrm{m}. The magnitude of component of vector \vec{A} along vector \vec{B} will be ____________ \mathrm{m}$.

Choose the correct answer: