Distance Of A Point From A Plane

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

%5Cvec%7Ba%7D%20%3D%203i%20%2B%204j%20%2B%205k

make angle

%5Ctheta

with z - axis, then it makes

90-%5Ctheta

with xy-plane, unit vector along z-axis is k.
So,

cos%5Ctheta%20%3D%20%5Cfrac%7B%5Cvec%7Ba%7D%2C%20%5Chat%7Bk%7D%7D%7B%5Cleft%7C%5Cvec%7Ba%7D%2C%5Cright%7C%5Ccdot%5Cleft%7C%5Chat%7Bk%7D%5Cright%7C%7D%20%3D%20%5Cfrac%7B%5Cleft(3i%20%2B%204j%20%2B%205k%5Cright).k%7D%7B%7C3i%20%2B%204j%20%2B%205k%7C%7D

%3D%20%5Cfrac%7B5%7D%7B5%5Csqrt%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%5CRightarrow%20%5Cquad%5Ctheta%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D

.
Hence angle with xy- plane

%5Cfrac%7B%5Cpi%20%7D%7B2%7D-%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%3D%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D

projection of

%5Cvec%7Ba%7D

on xy plane

%3D%20%7C%20%5Cvec%7Ba%7D%20%7C%20.cos%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D

%3D%205%5Csqrt%7B2%7D%20%5Ctimes%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%20%3D%205.

Chapter Questions
1 MCQs