Recall that given any vector v,v, we can calculate its length, |v|.|v|. Also, we say that two vectors that are scalar multiples of one another are parallel. Let v=⟨3,4⟩v=⟨3,4⟩ in R2.R2. Compute |v|,|v|, and determine the components of the vector u=1|v|v.u=1|v|v. What is the magnitude of the vector u?u? How does its direction compare to v?v? Let w=3i−3jw=3i−3j in R2.R2. Determine a unit vector uu in the same direction as w.w. Let v=⟨2,3,5⟩v=⟨2,3,5⟩ in R3.R3. Compute |v|,|v|, and determine the components of the vector u=1|v|v.u=1|v|v. What is the magnitude of the vector u?u? How does its direction compare to v?v? Let vv be an arbitrary nonzero vector in R3.R3. Write a general formula for a unit vector that is parallel to v.
Recall that given any vector v,v, we can calculate its length, |v|.|v|. Also, we say that two vectors that are scalar multiples of one another are parallel.
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Let v=⟨3,4⟩v=⟨3,4⟩ in R2.R2. Compute |v|,|v|, and determine the components of the vector u=1|v|v.u=1|v|v. What is the magnitude of the vector u?u? How does its direction compare to v?v?
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Let w=3i−3jw=3i−3j in R2.R2. Determine a unit vector uu in the same direction as w.w.
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Let v=⟨2,3,5⟩v=⟨2,3,5⟩ in R3.R3. Compute |v|,|v|, and determine the components of the vector u=1|v|v.u=1|v|v. What is the magnitude of the vector u?u? How does its direction compare to v?v?
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Let vv be an arbitrary nonzero vector in R3.R3. Write a general formula for a unit vector that is parallel to v.
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