Analytic Geometry Answers

Find the polar equations of the lines or curves whose Cartesian equations are
(a) (x x a)
2 + (y y a)
2 = a
2
(b) x
2/a2 + y
2/b2 = 1 (c) y = 2x (d) y = x
2
(e) xy = 4 (f) y = 4 (g) 3x x y + 2 = 0.

U= (-1,-7)
W= (3,1)
2U+(-3)w=

Find the Cartesian equations of the lines or curves whose polar equations are (a) r = a (b) r = a cos 2θ
(c) r2 = a2 sin 2θ (e) r = a sec(θ − α)

show that for any three vectors a,b,c
a×(b×c)+b×(c×a)+c×(a×b)=0

suppose A=3i-j-2k and B=2i+3j+k,Find |AxB|,(A+2B)x(2A-B),(A+B)x(A-B)

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

Consider the vectors
u = (1, 0) and v = (0, 1).
7.1 Determine cos θ, where θ is the angle between u and v. (4)
7.2 Determine the area of the parallelogram determined by u and v.

Let L1 and L2 be lines defined by
x = w0 + su, s ∈ R
and y = w1 + tv, t ∈ R, respectively.
Show that L1and L2 are parallel if and only if u = kv for some k ∈ R. (8)
8.2 Find the plane that passes through the point (2, 4, −3) and is parallel to
the plane −2x + 4y − 5z + 6 = 0. (4)
8.3 Find the line that passes through the point (2, 5, 3) and is perpendicular to the plane
2x − 3y + 4z + 7 = 0. (4)
8.4 Find an equation of the plane passing through the point(−2, 3, 4) and is perpendicular to the line
passing through the points (4, −2, 5) and (0, 2, 4).

If \\(a=3i-2j+k\\), \\(b=2i-4j-3k\\) and \\(c=-i+2j+2k\\), find the magnitude of \\(a+b+c\\)

Calculate the area of a triangle whose vertices are given by (3, -1, 2), (1, -1, 2)
and (4, -
2, 1).