Planes
Find a vector orthogonal to
x + 2y + 3z = 12
What is vec n = <1, 2, 3> ?
What vec n cdot vec m < 0 says about theta
What is "theta is obtuse" ?
vec u xx vec vis orthogonal to ________
What are "both
vec u and vec v" ?
(x/2)^2+(y/3)^2+(z/4)^2=1
What is the eqn. for an ellipsoid?
A unit vector for v = <3, 4, 5>
What is 1/sqrt(50)<3, 4, 5>?
The point (0,0,3) for
2x + 3y + 4z = 12
What is the z-intercept of the plane?
vec m cdot vec n = ?
(answer includes theta)
What is ||vec m|| ||vec n|| cos(theta)
?
|| m xx n || = ?
(answer includes theta)
What is ||vec m|| ||vec n|| sin(theta)?
z=(x/3)^2+(y/4)^2
What is the eqn. of an elliptic paraboloid?
Line p goes through (1,2,3) and (2,4,6). Equation?
What is "<1,2,3> + t<1,2,3>" ?
The intersection between
x + 2y + 3z = 10 and
2x + 4y + 6z = 50
What is { } ?
vec v cdot vec v =
What is ||vec v||^2 ?
vec k xx vec j =
What is -vec i ?
y=3x^2
What is the eqn. of a parabolic cylinder?
Line m = <1,2,3> + t<1,0,0>
Line p = <3,2,1> + t<0,0,1>
Their intersection?
What is the point
(3, 2, 3) ?
A plane has normal vector
<0,-1,0> and it contains the point (1,2,3).
Find the eqn. of the plane.
What is y = 2 ?
||vec m||=2sqrt(2), ||vec n||=3theta=(3pi)/4 vec m cdot vec n =
What is -6 ?
The connection between
||vec u xx vec v|| and geometry
How can you find the area of a parallelogram spanned by vec u and vec v ?
(x/2)^2+(y/3)^2-(z/4)^2=-1
What is the eqn. of a hyperboloid of 2 sheets?
Line m = <1,2,3> + t<1,0,0>
Line p = <3,2,1> + t<0,1,0>
Their intersection?
What is { } ?
The intersection between
x + 2y + 3z = 10 and
2x + 4y + 6z = 20
What is the plane
x + 2y + 3z = 10 ?
(vec u cdot vec v)/(vec v cdot vec v) vec v gives you this
What is the projection ofvec u onto vec v ?
The connection between
||vec u cdot (vec v xx vec w)|| and geometry
How can you find the volume of a parallelepiped spanned by vec u, vec v and vec w ?
(x/2)^2+(y/3)^2-(z/4)^2= 0
What is the eqn. of an elliptic cone?
Line m = <1,2,3> + t<3,2,1>
Line p = <4,4,4> + t<-3,-2,-1>
Their intersection?
What is "m and p are collinear" ?