Physics - Vectors Question with Solution | TestHub

Statement-2: The scalar projection (or component) of vector $\vec{A}$ onto vector $\vec{B}$ is defined as $\vec{A}\cdot \hat{B}$, where $\hat{B}$ is the unit vector in the direction of $\vec{B}$. This can be written as $\vec{A}\cdot \frac{\vec{B}}{|\vec{B}|}$. Thus, Statement-2 is true.

Statement-1: Using the formula from Statement-2, we calculate the component of $\vec{A}$ along $\vec{B}$.$\vec{A}\cdot \vec{B}=(2\hat{i}+3\hat{j}+\hat{k})\cdot (\hat{i}-\hat{j}+2\hat{k})=(2)(1)+(3)(-1)+(1)(2)=2-3+2=1$.$|\vec{B}|=\sqrt{(1{)}^2+(-1{)}^2+(2{)}^2}=\sqrt{1+1+4}=\sqrt{6}$. The component is $\frac{\vec{A}\cdot \vec{B}}{|\vec{B}|}=\frac{1}{\sqrt{6}}$. Thus, Statement-1 is true.

Statement-2 provides the correct formula used to calculate the component in Statement-1. Therefore, Statement-2 is a correct explanation for Statement-1.