18 flashcards · Shared on 19 August 2026 by AtomAI Library
Flip each card to check yourself.
Points A and B have position vectors (1, 2) and (4, −1). What is the vector AB?
(3, −3)
Points A and B have position vectors (1, 2) and (4, −1). What is the vector AB?
(3, −3)
In the parallelogram rule for vector addition, which line represents the sum of two vectors drawn from the same point?
The diagonal from the common starting point
What is (5, 2) − (1, −3)?
(4, 5)
For vectors a = (a₁, a₂) and b = (b₁, b₂), how is the dot product a · b calculated?
a₁b₁ + a₂b₂
Find the sum of the vectors (2, −1) and (3, 4).
(5, 3)
If v is a vector and k is a scalar, how are the magnitudes of v and kv related?
|kv| = |k||v|
Which is a unit vector in the direction of (3, 4)?
(3/5, 4/5)
Which formula gives the angle θ between two nonzero vectors a and b?
cos θ = (a · b)/(|a||b|)
For a nonzero vector b, which expression gives the vector projection of a onto b?
((a · b)/(b · b))b
What is the magnitude of the vector (3, 4)?
5
Which pair of nonzero vectors is parallel?
(2, −3) and (−4, 6)
If points have position vectors a and b, what is the position vector of their midpoint?
(a + b)/2
What is (1, 0, 0) × (0, 1, 0)?
(0, 0, 1)
Which statement best describes a vector?
A quantity with magnitude and direction
What is the result of multiplying the vector (3, −4) by the scalar −2?
(−6, 8)
Calculate (2, −1, 3) · (1, 4, −2).
−8
What must be true if two nonzero vectors have a dot product of zero?
They are perpendicular
Which statement describes the cross product a × b of two three-dimensional vectors?
It is perpendicular to both vectors and has magnitude |a||b| sin θ