for no2 intersects x axis if there is a point on it with y=
0 and z=0
Similarly for other 2 axes
Hi all, I have difficulty with these five questions about vector.
1. Find the coordinates of mirror image of A (3,1,2) when reflected in the plane x+2y+z=1.
(Do I have to find the foot of normal? But after that what should I do?)
2. Do the line through (3,4,-1) and normal to x+4y-z= -2 intersect any of the coordinate axes?
(After I find the equation of line how do I know if it intersects any axes?)
3. Show that the lines x -1 = (y-2)/2 = z+3 and x+1 = y-3 = 2z+5 are coplanar and find the equation of the plane which contains them.
4. A(1,2,-3/2) lies on the plane x+2y-2z=8. Find the coordinates of B such that vector AB is normal to the plane and 6 units from it.
The test is about to come and I am so worried about it...I hope someone can help me with solutions
Also is there any tips for the vector test? I am very bad in doing vectors...
Hello, hiy312!
Two lines are coplanar if they intersect.
We have: .
Equate coordinates: .
Solve the system of equations: .
The lines intersect at . . . They are coplanar.
The normal of the plane is perpendicular to both lines.
The lines have vectors: .
Hence: .
. . . . . .
The equation of the plane through with is:
. .