VITEEE 2018 Paper

xy-plane is perpendicular to z - axis. Let the vector
a = 3

^

i

+4

^

j

+5

^

k

make angle 0 with z - axis, then it makes 90-θ with xy-plane. unit vector along z-axis is k.
So, cos θ =

^ a . ^ k

| → a |.| → k |

=

(3i+4j+5k).k

|3i+4j+5k|

=

5

5√2

=

1

√2

⇒ θ =

π

4

Hence angle with xy- plane

π

2

−

π

4

=

π

4

projection of

→

a

on xy plane = |

→

a

| . cos

π

4

= 5√2 ×

1

√2

= 5