Question

A line is perpendicular to x+2y+2z=0 and passes through (0,1,0) . The perpendicular distance of the line from the origin is ?

Answer 1

oh the suspense ....

Answer 2

or is that the question .....

Answer 3

That is the complete question !

Answer 4

Better :D

Answer 5

pfft, now the suspense is gone lol

Answer 6

do you know what line is always perp to a plane?

Answer 7

by line i mean vector ... we will define the line using the vector and the stated point

Answer 8

The coefficients of x,y,z gives the direction ratio of the normal

Answer 9

Ah. :|
Sorry , please continue .

Answer 10

fine then, ill just take my brillant ideas and go make a sammich ....

oh you still need me then eh :)

Answer 11

yes, the coeffs

now we have a vector, we want another vector, specifically the one for the stated point to the origin

Answer 12

The equation of the line is (0,1,0) +k(1,2,2)

Answer 13

how do we determine the angle between 2 vectors?

Answer 14

Dot product..

Answer 15

there is a dotproduct equivalnce yes, namely:
\[|u|~|v|~cos(\alpha)=u\cdot v\]

Answer 16

sin(a) = d/h

d = h sin(a)

Answer 17

Yep ! Agreed.

Answer 18

Thanks a lot :D

Answer 19

so

vector form (0,1,0) to (0,0,0) = (0,-1,0) of length 1

vector of normal is (1,2,2) of length sqrt(9)=3

cos(a) = (0,-1,0).(1,2,2)/3

a = cos^(-1) (-2/3)

sin(a) = sin(cos^(-1) (-2/3))

and since our to the origin is a length of 1 it really not that important.

d = sin(cos^(-1)(-2/3))

Answer 20

good luck ;)