What is a line with magnitude (length/size) and direction?
100
Given p=(3 -2), q=(1 4) and r=(-2 -5) the vector of p-q-r is equal to this.
What is (4 -1)?
100
If p=(2, 3, -1) and q=(-1, 0, 2) then the angle between p and q is this.
What is 119 degrees?
100
Find the velocity vector of an object that is moving in the direction 3i-j with a speed of 20 km/h.
What is 2(radical 10)(3i-j)?
100
Line L has equation r=(3, -3)+t(2, 5) Write two other equations to represent line L.
What is x=3+2t, y=-3+5t, or 5x-2y=21?
200
The dot product of two vectors.
What is the sum of the products of the components of the vectors?
200
If A is (-1, 3, 2) and B is (2, 1, -4) then the magnitude of vector BA is this.
What is 7 units?
200
Find t such that a=(-1, 5) and b=(2, t) are perpendicular.
What t=2/5?
200
A yacht is sailing at a constant speed of 5(radical 10) km/h in the direction -i-3j. Initially it is at point (-6, 10). A beacon is at (0, 0) in the center of a tiny atoll. Find the time when the yacht is closest to the beacon.
What is 0.48h?
200
P (2, 0, 1), Q (3, 4, -2), and R(-1, 3, 2) are three points in space. Find the parametric equations of line (PQ)
What is x=2+t, y=4t, and z=1-3t?
300
The formula used to find length of a vector.
What is the distance formula.
300
Find k given that (-1/3, k) is a unit vector.
What is k=+/- (radical 8)/3?
300
Given that p=2i-j+4k and q=-i-4j+2k, find the dot product of p and q.
What is 10?
300
Find the vector equation of the line which cuts the y-axis at (0,8) and has direction 5i+4j.
What is (x,y)=(0,8)+t(5,4)?
300
Find the Cartesian equation of the line passing through (2, -3) with direction (4, -1)
What is x+4y=-10?
400
A set of equations that defines the coordinates of the dependent variables (x, y and z) of a curve or surface in terms of one or more independent variables.
What is a parametric equation?
400
Find r and s given that a=(2, -1, r) is parallel to b=(s, 2, -3)
What is r=3/2 and s=-4?
400
Suppose u=2i+j, v=3j, and theta is the acute angle between u and v. Find the exact value of sin theta.
What is 2/radical 5?
400
Find the vector equation of the line that passes through (-6,3) with direction (4, -3).
What is (x,y)=(-6,3)+t(4,-3)
400
Classify the following line pairs as either parallel, intersecting, or skew, and find the measure of the acute angle between them: x=2+t, y=-1+2t, z=3-t and x=-8+4s, y=s, z=7-2s.
What is intersecting at (4,3,1) with angle approximately 44.5 degrees?
500
Algebraic equations involving the coordinates of the points lying on the shape.
What is a cartesian equation?
500
a, b, and c are this if (a-3, b-2, c-1)=(1-a,-b,-3-c)
What is a=2, b=1, and c=-1?
500
For p=(-1, 2, 1) and q=(3, -1, 4) find the dot product of p and q.
What is -1?
500
Triangle ABC is formed by three lines: Line AB is (x,y)=(4,-1)+t(1,3), line BC is (x,y)=(7,4)+s(1,-1), and line AC is (x,y)=(-1,0)+u(3,1). Use vector methods to find the coordinates of A, B, and C.
What is A(5,2), B(6,5), and C(8,3)?
500
Find the angle between the lines L1 x=1-4t, y=3t and L2 x=2+5s, y=5-12s.