Let A = (0,0), B = (3,0), C = (2,8). Find a point P such that...
Let A = (0,0), B = (3,0), C = (2,8). Find a point P such that AP
is perpendicular BC, BP is perpendicular to AC, and CP is
perpendicular to AB. Does it surprise you that such a point
exists?
Let P be the point (2, 3, -2). Suppose that the point P0(-3, -2,
7) is...
Let P be the point (2, 3, -2). Suppose that the point P0(-3, -2,
7) is 1/4 of the way from P to Q. Find the point Q.
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b
onto a....
1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b
onto a. proj a b=
2) Find the area of a triangle PQR, where P=(−2,−4,0),
Q=(1,2,−1), and R=(−3,−6,5)
3) Complete the parametric equations of the line through the
points (7,6,-1) and (-4,4,8)
x(t)=7−11
y(t)=
z(t)=
1.
(1 point)
Find the distance the point P(1, -6, 7), is to the plane through...
1.
(1 point)
Find the distance the point P(1, -6, 7), is to the plane through
the three points
Q(-1, -1, 5), R(-5, 2, 6), and S(3, -4, 8).
2.
(1 point) For the curve given by
r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉,
Find the derivative
r′(t)=〈r′(t)=〈 , , 〉〉
Find the second derivative
r″(t)=〈r″(t)=〈 , , 〉〉
Find the curvature at t=1t=1
κ(1)=κ(1)=
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize
L. Find the point Q...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize
L. Find the point Q where L intersects the xy-plane.
b) Find the angle that the line through (0,-1,1) and (√3,1,4)
makes with a normal vector to the xy-plane.
c) Find the distance from the point (3,1,-2) to the plane
x-2y+z=4.
d) Find a Cartesian equation for the plane containing (1,1,2),
(2,1,1) and (1,2,1)
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.
Find the shortest distance from the point P = (−1, 2, 3) to the
line of...
Find the shortest distance from the point P = (−1, 2, 3) to the
line of inter- section of the planes x + 2y − 3z = 4 and 2x − y +
2z = 5.
2. Let P 1 and P2 be planes with general equations P1 : −2x + y...
2. Let P 1 and P2 be planes with general equations P1 : −2x + y
− 4z = 2, P2 : x + 2y = 7.
(a) Let P3 be a plane which is orthogonal to both P1 and P2. If
such a plane P3 exists, give a possible general equation for it.
Otherwise, explain why it is not possible to find such a plane. (b)
Let ` be a line which is orthogonal to both P1 and P2....