Analytic Geometry Answers

Find the vector that has (a) the same direction as A and twice the magnitude of A, (b) the opposite direction of a and one-third the magnitude of a, and (c) the same direction as A and magnitude 2.

(i)A=14i-15j+6k

Determine the equation of the plane containing the points P(1,3,2) Q=(-2,0,-2) and R=(1,4,3)

Find the parametric equations for the line L through P(5,-2,4) that is parallel to (1/2, 2, -2/3)

(i) where does line L intersect the xy- plane?

(ii) sketch the position vector for a and the line L.

1.Discuss the graph of the equation x^2 +y^2 + z^2 -6x +8y+4z+4=0

1. Find the midpoint of the segment with ends (4, -3, 1) and (-2, 5, 3).

2. Determine whether the vectors u=3i+j-2k and v=2i-4j+k are orthogonal.

3. Describe and sketch 9x^2 + 9y^2 - 4z^2=0

ABCD is a quadrilateral with coordinates A (-5,2), B (6,2), C (1,-5), and D (-2,-3). Find the verticals of A'B'C'D under the translation (X+3,y - 6).

what is the equation of a circle passing through (6,2) and tangent to the line x-4y-15=0 at (3,-3)

A single-lane street 10 ft wide goes through a semicircular tunnel with radius 9 ft. How high is the tunnel at the edge of each lane? Roun off to 2 decimal places.

Find the equation of the line tangent to the circle with the center at (-1,1) and point of tangency at (-1,3).

Show that if B>0, then the graph of x²+Bxy=F, is a hyperbola if F≠0, and two intersecting lines if F=0.