The angle between a line and a plane is found by finding angle between the line and normal to the plane. Since one would know both the vectors we can fond the angle by finding the dot product of the vectors.
Hi if i was needing to find the angle between the plane
P:r = (0,0,1) + lambda(1,1,0) + mu(0,1,2)
and the line
L: z=0, y=4x+1
I think the equation of the line would be (1, 5 0)
and i believe that the plane is bounded by the direction vectors (1,1,0) and (0,1,2)
I was told be a friend to try and use the trig identity of cos(pi/2 -x) = sin x
any help or just a push in the right direction for this would be greatly appreciated
You mean a vector in the direction of the line. You are mistaken. Perhaps it would be easier if the line were written as
x= t, y= 4t+ 1, z= 0.
[quote]and i believe that the plane is bounded by the direction vectors (1,1,0) and (0,1,2) [quote]
"Bounded" is the wrong word here- a plane has no "boundaries". (1, 1, 0) and (0, 1, 2) are vectors [b]in the plane and so their cross product is perpedicular to the plane.
As ibdutt said, the angle between a line and a plane is the angle between a vector in the direction of the line and a vector perpendicular to the plane. And that can be calculatedI was told be a friend to try and use the trig identity of cos(pi/2 -x) = sin x
any help or just a push in the right direction for this would be greatly appreciated
using . There is nothing here that involves changing from sine to cosine or vice versa.
I have a different take on this question.
In most cases when speaking of the angle between a line and a plane, usually that is understood to be an acute angle (the line is not parallel to the plane).
Notation:
is a plane and is a line such that .
Thus the acute angle between is
The answer depends upon how one defines the angle between a line and a plane.
The answer above is not the answer used in most vector geometry textbooks.
is the obtuse angle between the plane's normal and the given line's direction.
But that does not seen natural to use as the meaning for the angle between a line and a plane.
So how does your textbook/lecturenotes define that term?
But again, that is the acute between the normal and the line,
That is not the usual meaning between a line and a plane.
See reply #5.
The normal is perpendicular to the plane. Does it seem natural to take the angle between the line and the normal as the angle between the line and the plane?
But what does your text material say about it? Surely it is defined (explained) somewhere in your notes.
Yes when examining your point it does make intuitive sense , I have been searching through my notes for some form of definition but nothing is there to define it. So the 119.017 I have calculated is the angle between the normal to the plane and line. I understand why I must find the angle between the line and the plane but I am not sure how to utilize the formula shown in your response #5. Could you elaborate how to use this.
I really do not remember the details of this question,
Do you understand the operations in the formula
If you do, then is the normal of the given plane and is the direction of the given line.
Just apply. You should get a value between
BTW I absolutely refuse to use degrees.