# Acute angle between a plane and y axis

• Oct 28th 2012, 09:53 AM
nks2427
Acute angle between a plane and y axis
Hey guys. The question goes like this :

Coordinates of A(-1,2,5) and B(2,-2,11). Plane p passes through B and is perpendicular to AB. It is required to find
(a) Equation of plane p
(b) Acute angle between plane p and y axis.

An equation for p is 3x - 4y + 6z = 80

What is the next step to calculate the angle ?

i use the formula cos θ = A . B / |A| x |B| ,

i can substitute the value of A with normal vector of plane p. Then how should i proceed? Is there a direction vector for the y axis ??

• Oct 28th 2012, 10:55 AM
Plato
Re: Acute angle between a plane and y axis
Quote:

Originally Posted by nks2427
Hey guys. The question goes like this :
Coordinates of A(-1,2,5) and B(2,-2,11). Plane p passes through B and is perpendicular to AB. It is required to find
(a) Equation of plane p
(b) Acute angle between plane p and y axis.
An equation for p is 3x - 4y + 6z = 80
What is the next step to calculate the angle ?

Given a plane $N\cdot(R-P)=0$ and line $Q+tD$ if the line is not parallel to the plane, i.e. $N\cdot D\ne 0$, then the acute angle between the line and the plane is the complement of the acute angle between $D~\&~N$.

In this case $D=<0,1,0>~\&~N=<3,-4,6>$.
• Oct 28th 2012, 11:48 AM
nks2427
Re: Acute angle between a plane and y axis
can D be taken as D = < 0, 2 , 0 > ?
• Oct 28th 2012, 11:57 AM
Plato
Re: Acute angle between a plane and y axis
Quote:

Originally Posted by nks2427
can D be taken as D = < 0, 2 , 0 > ?

Yes. Any vector parallel to the y-axis.
• Oct 28th 2012, 11:34 PM
nks2427
Re: Acute angle between a plane and y axis
Thank you :DD
• Apr 17th 2017, 05:53 AM
Jasmine17
Re: Acute angle between a plane and y axis
Hi, why is D = < 0,1,0> ?
• Apr 17th 2017, 07:25 AM
Plato
Re: Acute angle between a plane and y axis
Quote:

Originally Posted by Jasmine17
Hi, why is D = < 0,1,0> ?

That is parallel to the $y$-axis.