Analytic Geometry Answers

Find the unit vector that is perpendicular to vectors A=2i + j + k and B= -1 + 2j + k

Given that A(2,3,-1) and B(1,2,4) are points in space. Find the unit vector along the direction of AB and the one along BA. Also find the position vector of the point C which is on the mid-point of AB

A parabola given by x = ay2 + by + c passes through points (1,2) , (-3,2) and (-2,4) .

1. Find the equation ?

2. Determine whether the line x + 2y + 3 = 0 is tangent to the parabola in (1)

3. Show that each point P(x,y) on the parabola is equidistant from (-2,2) and the line x= -4

Find the vector joining the points P(2, 3, 0) and Q(-1, -2, -4) directed from P to Q.

Select one:

A. 3i-5j-4k

B. 3i-5j+4k

C. 3i+5j-4k

D. -3i-5j-4k

Consider the conic represented by 4(x²+2y)=9. Now shift the origin to (1,-1) and then rotate the axes through π/3 What is the resultant equation? What geometrical object does it represent?

Find a unit vector perpendicular to the plane through P(2, 1, -1), Q(-1, 1, 2) and R (1, -1, 2)

Let u=(-5, -2, 4), v= (3, 6, -5) and w = (-7, 1, -8)

a) Calculate (u × v).w and hence find the volume of the parallelepiped with adjacent sides u, v, and w.

b) Show that vector (u - proj_wu) and w are orthogonal.

c) Use the cross product to find the angle between u and w.

Determine the equation of the circle with radius 9

9 and center (-1,-8)

(−1,−8).

To find a missing side length set up and solve a ____________________. Put the measurements of the smaller figure on top and the bigger figure on the bottom.