The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis is: (0, -1/2, √3/2).
<h3>Vector</h3>
a. Vector (v)
Vector (v)=v (cos Ф, sin Ф)
V=1 while the counterclockwise angle that is measured from positive x=Ф=π/4
Hence:
Vector=3(cos π/4, sinπ/4)
Vector=(3/√2, 3√2)
b. Vector w:
Vector w=1(0, cos 2π/3, sin2π/3)
Vector w=(0, -1/2, √3/2)
Therefore the vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis is: (3/√2, 3√2) and The vector ws: (0, -1/2, √3/2).
The complete question is:
Resolve the following vectors into components:
a. The vector v in 2-space of length 3 pointing up at an angle of π/4 measured from the positive x-axis.
(b) The vector w in 3-space of length 1 lying in the yz-plane pointing upward at an angle of 2π/3 measured from the positive y-axis.
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