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. 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. 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.
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.
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.
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