a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0...
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).
1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3,...
1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3, 0) answer the following questions • What is the distance
between P and Q? • Determine the vectors P Q~ and P R~ ? • Find the
dot product between P Q~ and P R~ . • What is the angle between P
Q~ and P R~ ? • What is the projP R~ (P R~ )? • What is P Q~
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and...
Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.
Suppose g: P → Q and f: Q → R where P = {1, 2, 3,...
Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4},
Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by
f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4,
b)}.
(a) Is Function f and g invertible? If yes find f −1
and g −1 or if not why?
(b) Find f o g and g o...
Let P be the plane given by the equation 2x + y − 3z = 2....
Let P be the plane given by the equation 2x + y − 3z = 2. The
point Q(1, 2, 3) is not on the plane P, the point R is on the plane
P, and the line L1 through Q and R is orthogonal to the plane P.
Let W be another point (1, 1, 3). Find parametric equations of the
line L2 that passes through points W and R.