18 flashcards · Shared on 19 August 2026 by AtomAI Library
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Which statement best describes a vector?
A quantity with magnitude and direction
Which statement best describes a vector?
A quantity with magnitude and direction
Points A and B have position vectors (1, 2) and (4, −1). What is the vector AB?
(3, −3)
What is the magnitude of the vector (3, 4)?
5
Find the sum of the vectors (2, −1) and (3, 4).
(5, 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)
What is the result of multiplying the vector (3, −4) by the scalar −2?
(−6, 8)
If v is a vector and k is a scalar, how are the magnitudes of v and kv related?
|kv| = |k||v|
Which pair of nonzero vectors is parallel?
(2, −3) and (−4, 6)
Which is a unit vector in the direction of (3, 4)?
(3/5, 4/5)
If points have position vectors a and b, what is the position vector of their midpoint?
(a + b)/2
For vectors a = (a₁, a₂) and b = (b₁, b₂), how is the dot product a · b calculated?
a₁b₁ + a₂b₂
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 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
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
What is (1, 0, 0) × (0, 1, 0)?
(0, 0, 1)