Question

Find the projection of vector \(\hat i+3\hat j+7\hat k\) on vector \(7\hat i-\hat j+8\hat k\).

Hint:

Projection of a on b equals (a.b)/|b|; compute the dot product and the magnitude of b.

Answer 1

Step 1: Dot product, matching components in order:
$1\times7=7$, $3\times(-1)=-3$, $7\times8=56$; total $7-3+56=60$.

Step 2: Magnitude of the vector being projected onto:
$|7\hat i-\hat j+8\hat k|=\sqrt{49+1+64}=\sqrt{114}$.

Step 3: Divide:
Projection $=\dfrac{\vec a\cdot\vec b}{|\vec b|}=\dfrac{60}{\sqrt{114}}$.

Final Answer:
\[ \boxed{60/\sqrt{114}} \]