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Analytic Geometry
4. What is the distance between the point (1,2,4) and the plane 3x+ 2y+ 6z= 5?
5. What is the distance between the parallel planes ax+by+cz=d1 and ax+by+cz=d2?
You may wish to try picking a point on one plane that you can specify exactly and
working out the distance from that point to the other plane.
5. What is the distance between the parallel planes ax+by+cz=d1 and ax+by+cz=d2?
You may wish to try picking a point on one plane that you can specify exactly and
working out the distance from that point to the other plane.
Analytic Geometry
3. What is the cosine of the angle between the plane x+y+z= 5 and any of the
coordinate planes? What about the cosine of the angle between x+y+z= 5 and
x+ 2y+ 3z= 5?
coordinate planes? What about the cosine of the angle between x+y+z= 5 and
x+ 2y+ 3z= 5?
Analytic Geometry
2. Assume that A=<ax,0,0>, B=<bx,by,bz>, and C=<cx,cy,cz>, and demonstrate that
the following vector identity holds:
Ax(BxC) = (A.C)B-(A.B)C
Note that if you replace the subscript "x" by "i", "y" by j, and "z" by k, and then cycle
x->y->z->x appropriately, you've proven the identity is true in general.
the following vector identity holds:
Ax(BxC) = (A.C)B-(A.B)C
Note that if you replace the subscript "x" by "i", "y" by j, and "z" by k, and then cycle
x->y->z->x appropriately, you've proven the identity is true in general.
Analytic Geometry
1. Find the volume of the parallelpiped spanned by the vectors
A=i+j-k; B= i-j+k; C=-i+j+k.
A=i+j-k; B= i-j+k; C=-i+j+k.
Analytic Geometry
Suppose u and v are vectors in 3–space where u = (u1, u2, u3) and v = (v1, v2, v3). Evaluate u×v×u and v × u × u.
Analytic Geometry
given that r1=3i-2j+k, r2=2i-4j-3k, r3=-i+2j+2k, the direction of cosines of the vector (r1+r2+r3) is
Analytic Geometry
find the midpoint
(-2 7/8, 5/8), (-3 1/4, 1/2)
(-2 7/8, 5/8), (-3 1/4, 1/2)
Analytic Geometry
Determine whether each of the following points is inside, outside or on the circle with equation x^2+y^2=5
(0,-√5)
(0,-√5)
Analytic Geometry
Find the distance between the following pair of points
A) the origin and (-√3,√6)
A) the origin and (-√3,√6)
Analytic Geometry
Determine whether each of the following points is inside, outside, or on the circle with equation x^2+y^2=5.
A) (-1,2)
B) (3/2,2)
C) (-1,3/2)
A) (-1,2)
B) (3/2,2)
C) (-1,3/2)
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#340153 on Dec 2023
#340153 on Dec 2023