Statement-1: If $\vec a=\hat i+\hat j+\hat k$ and $\vec b=2\hat i+2\hat j$, then component of $\vec a$ orthogonal to $\vec b$ is $\hat k$.
Statement-2: Component of $\vec a$ along $\vec b=\frac{(\vec a.\vec b)}{|\vec b|^2}\vec b$ and component of $\vec a$ orthogonal to $\vec b$ is $\vec a-(\frac{\vec a.\vec b}{|\vec b|^2})\vec b$.
Answer & explanation
Correct answer: option 1
Clearly, statement-2 is true.
We have, $\vec a.\vec b=2+2=4, |\vec b|^2=8$
Using statement-2, we have
Component of $\vec a$ orthogonal to $\vec b=\vec a-\frac{(\vec a.\vec b)}{|\vec b|^2}\vec b$
$=\vec a-\frac{1}{2}\vec b$
$=(\hat i+\hat j+\hat k)-(\hat i+\hat j)=\hat k$
So, statement-1 is true.
Also, statement-2 is a correct explanation for statement-1.