Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z) = (-7t,7t,1t). The distance is=?
Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z) = (-7t,7t,1t). The distance is=?
You are looking down at a map. A vector U with |U| 1 points north and a vector V with |V|= 9 points northeast. The crossproduct UxV points: A) south? B) northwest? C) up? D) down...
Among all the unit vectors u= <x,y,z> in R3, find the one for which the sum x + 2y + 5z is minimal. u=<>?
If vec{v} times vec{w} = <2,5,4> and vec{v}•vec{w} = 2, find tan(theta), where theta is the angle between vec{v} and vec{w}. tan(theta)=
Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-5, -5, -4), Q = (-1, -1, 0), and R = (-1, -1, 5).
Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z)= (-7 t, 7 t, 1 t). the distance is:
Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way
Find the point P where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = -3.
Consider the two lines L1: x = -2t, y = 1 + 2t, z = 3t and L2: x = -9 + 5 s, y = 5 s, z = 2 + 4 s Find the point of intersection of the two lines....
Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way
Let A = (4, 2, -4), B = (0, 1, -1), C = (5, 7, 0), and D = (1, 6, 3). Find the area of the parallelogram determined by these four points, the area of the triangle ABC, and the area of the triangle...
Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way
Find the volume of the parallelepiped with one vertex at (-5, -1, 1), and adjacent vertices at (-3, 3, -5), (-1, 3, -1), and (-4, 4, 6). volume?
Find a and b such that [18,24,13] = a [1,-2,1] + b [4,4,3]. a=? b=?
Perform the following operations on the vectors vec{u} =<4,-4,4>, vec{v}=<4,2,-4>, and vec{w} =<0,-2,-1>. (u)•vec(w)= (u•v)u= ((w•w)u)•u= u•v...
Find the angle between the vectors [-3 3] and [-5 5]
Let u=(1,-1,0) and v=(1,-2,-3). Find the vector w=2u-3v and its additive inverse. w= -w=
Let x = [-4, 4,5] and y=[0,0,-3] Find the dot product of x and y x.y=?
Find the angle between the vectors [1 4 -5] and [5 -5 4]
Find all 2x2 matrices A that are symmetric and whose squares are equal to themselves