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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)
Analytic Geometry
Find the distance between the following pair of points
A) (-1,0) and (3,0)
B) (1,-2) and (1,4)
C) (-2,3) and (2,0)
E) (a,a) and (-a,-a)
F) (a,b) and (-a,-b)
A) (-1,0) and (3,0)
B) (1,-2) and (1,4)
C) (-2,3) and (2,0)
E) (a,a) and (-a,-a)
F) (a,b) and (-a,-b)
Analytic Geometry
A circle passes through the points A(-1,2),B (3,4) C(2,3).determine it's equation
