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Angles and projectionsa. Find the angle between u and v.b.
Chapter 12, Problem 19RE(choose chapter or problem)
Angles and projections
(a) Find the angle between u and v.
(b) Compute \(\operatorname{proj}_{\mathrm{v}} \mathbf{u}\) and \(\mathrm{scal}_{\mathrm{v}} \mathbf{u}\).
(c) Compute \(\operatorname{proj}_{\mathrm{u}} \mathbf{v}\) and \(\mathrm{scal}_{\mathrm{u}} \mathbf{v}\).
u=6i-k, v=8i+2j-3k
Questions & Answers
QUESTION:
Angles and projections
(a) Find the angle between u and v.
(b) Compute \(\operatorname{proj}_{\mathrm{v}} \mathbf{u}\) and \(\mathrm{scal}_{\mathrm{v}} \mathbf{u}\).
(c) Compute \(\operatorname{proj}_{\mathrm{u}} \mathbf{v}\) and \(\mathrm{scal}_{\mathrm{u}} \mathbf{v}\).
u=6i-k, v=8i+2j-3k
ANSWER:Solution 19REStep 1:a) Given vectors are u = 6i -k , v = 8i + 2j -3k.Angle between the two vectors u , and v is ; cos(= Therefore , angle between u = 6i -k , v = 8i + 2j -3k is ; cos(= = = = 0.955485Therefore,