Question

The projection of vector \( \vec{a} = 2\vec{i} + 3\vec{j} + 2\vec{k} \) on vector \( \vec{b} = \vec{i} + 2\vec{j} + \vec{k} \) is:

• A. $\frac{10}{\sqrt{6}}$
• B. $\frac{5}{\sqrt{6}}$
• C. $\frac{10}{3}$
• D. $\frac{5}{3}$

Hint:

Projection is a scalar value representing the "shadow" of one vector on another.

Answer 1

The Correct Option is A

Step 1: Concept
Projection of $\vec{a}$ on $\vec{b} = \frac{\vec{a} \cdot \vec{b}}{|\vec{b}|}$.
Step 2: Analysis
$\vec{a} \cdot \vec{b} = (2)(1) + (3)(2) + (2)(1) = 2 + 6 + 2 = 10$. $|\vec{b}| = \sqrt{1^{2} + 2^{2} + 1^{2}} = \sqrt{6}$.
Step 3: Conclusion
Projection $= 10 / \sqrt{6}$.
Final Answer: (A)