WorksheetsVectors
Total questions: 16
Worksheet time: 25mins
A vector quantity has____ and ____
(a)
Direction 24.4° Magnitude 24.2
Direction65.6° Magnitude 24.2
Magnitude 12.1
Magnitude 12.1
Find 3u - 2v
15
<21,-6>
-15
<-21,6>
A river flows due south at 3 mi/h. A swimmer attempting to cross the river heads due east swimming at 2 mi/h relative to the water. Find the true speed and direction of the swimmer.
3.6 mi/hr, -3/2 degrees
<2,-3>, 56.3 degrees
<2,-3>, -56.3 degrees
3.6 mi/hr, 303.7 degrees
The dot product is a ___ quantity
Vector
Scalar
Are the given vectors orthogonal?
Yes, the angle between them is 0 degrees.
Yes, the angle between them in 90 degrees.
No, the angle between them is 30 degrees.
No, the angle between them is 60 degrees.
The dot product can be used with two and three dimensional vectors
I agree
I disagree
It depends
Not sure
Find the distance between points P(1,2,-1) and Q(3,-1,2)
312
22
7
49
The equation (x−1)2+(y+2)2+(z−4)2=2 represents a sphere with center C(1,-2,4) and radius 2
I agree
I disagree
It depends
I'm not sure
The cross-product can be used in both two and three dimensions
I agree
I disagree
It depends
Not sure
Find the cross product.
(a)
<0,-9,9>
<-5,1,1>
9 2
4 3
The equations x = 5 +2t, y = 2- t, and z = 8 + 5t pass through P and are parallel to v.
True
False
It depends
Not sure
Find all parametric equations that pass through P and Q.
x = 1 + 2t
y = -4t
z = 2t
x = 3 + 2t
y = -4 - 4t
z = 2 + 2t
x = 1 + 4t
y = -3t
z = 5t
x = 3 + 4t
y = -4 - 3t
z = 2 + 5t
Find an equation for the plane with normal vector n = <2,3,-5> and passing through point P(2,1,1) and simplify.
(a)
Find the direction angle β of the vector v = <1,2,3>
74 degrees
58 degrees
37 degrees
101 degrees
