Froggy Jumps
Vectors III Lowersixth Science MathematicsOnline version
Cross and line concepts for vectors.
1
What is the magnitude of the cross product |a × b| equal to when a ⟂ b and |a|=4, |b|=3?
2
The cross product a × b is perpendicular to which of the following?
3
If a × a = 0, what does this imply about vectors a and a?
4
Which property is false for the cross product?
5
Compute the cross product magnitude: |i × j| = ?
6
Which operation yields a vector perpendicular to both a and b?
7
Triple scalar product [a · (b × c)] represents what?
8
The triple product [a · (b × c)] changes sign if which is swapped?
9
What is (a × b) · c equal to in general?
10
If a × b is zero, what can be inferred about a and b?
11
Cross product is defined in which dimension?
12
The component form of a × b uses which symbol for unit vectors?
13
Given a = (a1,a2,a3) and b = (b1,b2,b3), the x-component of a × b is?
14
The y-component of a × b is given by?
15
The z-component of a × b is?
16
If a = (1,0,0) and b = (0,1,0), a × b equals?
17
Which property holds: a × (b + c) = a × b + a × c?
18
Is (λa) × b equal to λ(a × b) for scalar λ?
19
Which operation gives a vector along the normal to the plane of a and b?
20
If a and b are parallel, what is |a × b|?
21
What does the cross product with itself yield?
22
Which is not a property of a × b?
23
The magnitude of a × b equals |a||b|sinθ, where θ is the angle between?
24
If a and b are orthogonal, |a × b| = ?
25
What does the triple product [a · (b × c)] geometrically represent?
26
What is the scalar value of (a × b) · a?
27
Line in space that passes through a point p with direction d is called?
28
If two lines in space are parallel, their direction vectors are?
29
Two skew lines are defined as lines that are:
30
Direction vector of a line in space is:
31
The distance from a point to a line in 3D can be found using which method?
32
The cross product of two parallel vectors is:
33
If a, b, c are non-coplanar, the triple product [a · (b × c)] is:
34
Which statement is true for lines in space?
35
The cross product is defined as a × b perpendicular to the plane of:
36
If a, b, c are vectors, the volume of the parallelepiped is given by:
37
The area of the parallelogram spanned by a and b is:
38
Which is a scalar result from vector operations?
39
The cross product a × b is zero when a and b are:
40
If a = (1,2,3) and b = (4,5,6), the x-component of a × b is?
41
The equation of a line in symmetric form is:
42
Two lines r = p + t d and s = q + u e intersect if the system has:
43
Which is not a type of line relation in space?
44
A line's direction vector is used to:
45
If a, b, c are linearly independent, the triple product:
46
The vector product (a × b) is:
47
Which operation yields a scalar, not a vector?
48
Dividing a line segment uses which concept?
49
Which property of the vector cross product means a×b = - (b×a)?
50
If two vectors are parallel, what is a×b?
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Functions and Structures of the skin
