(a) Draw a picture that shows the direction angles α , β , and γ of a vector. (b) What are the components of a unit vector in 2-space that makes an angle of 120 ∘ with the vector i (two answers)? (c) How can you use vectors to determine whether a triangle with known vertices P 1 , P 2 , and P 3 has an obtuse angle? (d) True or false: The cross product or orthogonal unit vector is a unit vector. Explain your reasoning.
(a) Draw a picture that shows the direction angles α , β , and γ of a vector. (b) What are the components of a unit vector in 2-space that makes an angle of 120 ∘ with the vector i (two answers)? (c) How can you use vectors to determine whether a triangle with known vertices P 1 , P 2 , and P 3 has an obtuse angle? (d) True or false: The cross product or orthogonal unit vector is a unit vector. Explain your reasoning.
(a) Draw a picture that shows the direction angles
α
,
β
,
and
γ
of a vector.
(b) What are the components of a unit vector in 2-space that makes an angle of
120
∘
with the vector i (two answers)?
(c) How can you use vectors to determine whether a triangle with known vertices
P
1
,
P
2
,
and
P
3
has an obtuse angle?
(d) True or false: The cross product or orthogonal unit vector is a unit vector. Explain your reasoning.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Thomas' Calculus: Early Transcendentals (14th Edition)
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