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: Recall the projection formula:
Projection of \(\vec a\) on \(\vec b\) is \(\dfrac{\vec a\cdot\vec b}{|\vec b|}\).

Step 2: Compute the dot product:
\[ (1)(7)+(3)(-1)+(7)(8)=7-3+56=60 \]

Step 3: Compute \(|\vec b|\):
\[ |\vec b|=\sqrt{7^2+(-1)^2+8^2}=\sqrt{49+1+64}=\sqrt{114} \]

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