Answer:
Option B
Explanation:
xy-plane is perpendicular to z - axis. Let the vector
$\vec{a}$ = 3i + 4j + 5k make angle θ with z - axis, then it makes 90 - θ with xy-plane. unit vector along z-axis is k.
So, cos θ = $\frac{\vec{a}\hat{k}}{|\vec{a}|.|\hat{k}|}$
= $\frac{(3i + 4j + 5k).k}{|3i+4j+5k|}$ = $\frac{5}{5\sqrt{2}}$ = $\frac{1}{\sqrt{2}}$ →θ = $\frac{\pi}{4}$
Hence angle with xy - plane $\frac{\pi}{2}-\frac{\pi}{4}=\frac{\pi}{4}$
projection of $\vec{a}$ on xy-plane $|\vec{a}|.\cos\frac{\pi}{4}$ = $5\sqrt{2}\times\frac{1}{\sqrt{2}}=5$
