Analytic Geometry Answers

if a,b,c be three unit vector sch that ax(bxc)=b/2.
Find the angle which a makes with b & c , B & c being non- parallel.

how to reduce 2xsquared-3ysquare-6x+12y to standard form of a hyperbola

1.For The Vector a b c and d show that :
(axb).(cxd)+(bxc).(axd)+(cxa).(bxd)=o
2.Find Two Unit vector Perpendicular to both
A=i-2j+3k
B= -2i+4j

A soccer ball has 12 pentagons and 20 hexagons, making a perfect ball shape; I'm told that any other combination of polygon that also form a ball shape MUST have 'at least' 12 pentagons, yet I have a photo of a ball shaped with close to 90 hexagons and possibly ONLY 6 pentagons. I will email the photo if you wish to work out the exact numbers ... then tell me if you can how it can work with only 6 pentagons -- please.

The hypotenuse of a right triangles its ends at the points(1,3) and (-4,1). Find the equation of the legs (perpendicular sides ) of the triangle.

1. At the half time show, a marching band marched in formation. The lead drummer started at a point with coordinates (-2,-5) and moved 3 steps up and 1 step right.

Write a rule to describe the translation.
What were the coordinates of the drummer's final position?

If c-a=mb then: cot(C-A)/2=(1+mcosC)/ (msinC). How?

A negative vector could be denoted as
a)w,w
b)a,b
c)u,v
d)u,-u

Addition property of equality :AB=5,then 10+AB=?

(a) Have C be a circular region in R^2. Determine the normal cone for a point on its circumference.
(b) Have C be a rectangular region in R^2. Determine the normal cone for a point on its boundary.