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Fill in the blank:
If vectors A and B are orthogonal, then the value of their dot product is ________.
0
1
-1
Is this statement true or false?
If vector A = [3, -2, 1] and vector B = [1, 2, 3], then they are orthogonal.
True
False
In a 2D Cartesian coordinate system, the pair [0, 2] and [2, 0] of vectors are ________.
Orthogonal
Parallel
Double
None
If vectors A, B, and C are pairwise orthogonal, which of the following is true?
A + B = C
A - B = C
A + B + C = 0
A × B = C
If vector A is orthogonal to both vector B and vector C, then the relationship between vectors B and C are ________.
Orthogonal to each other
Linearly dependent
Opposite directions
In a 3D space, if vector A is orthogonal to vectors B and C, which of the following is true?
A is parallel to the plane defined by B and C.
A is perpendicular to the plane defined by B and C.
A lies on the line defined by the cross product of B and C.
Which of the following pairs of vectors are orthogonal?
[2, 0, -1] and [1, 2, 1]
[0, 1, 0] and [0, 0, 1]
[1, 1, 1] and [1, -1, 1]
[3, 4] and [-4, 3]
In a 3-dimensional space, two vectors are orthogonal to the vector [1, -2, 3].
If two vectors are orthogonal, what can you say about the angle between them?
The angle is acute.
The angle is obtuse.
The angle is 90 degrees.
The angle is 180 degrees.
Given two non-zero vectors A and B, if their dot product is zero, what can be concluded?
A and B are parallel.
A and B are anti-parallel.
A and B are orthogonal.
A and B are collinear.
It is done.