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9.2: Calculating Vector Length, Normalization, Distance and Dot


In this section we will cover some of the basic vector math we will use this semester.

Do This

Watch the following summary video about calculation of vector length, Normalizing vectors and the distance between points then answer the questions.

Vector:

[(a_1, a_2, dots a_n) onumber ]

[(b_1, b_2, dots b_n) onumber ]

Length:

[length = sqrt{a_1^2 + a_2^2 + dots + a_n^2} onumber ]

Normalization:

[frac{1}{length}(a_1, a_2, dots a_n) onumber ]

Distance:

[distance = sqrt{(a_1 - b_1)^2 + (a_2 - b_2)^2 + dots + (a_n - b_n)^2} onumber ]

Question

Calculate length of vector (4.5, 2.6, 3.3, 4.1)?

Question

What is a normalized form of the vector (4.5, 2.6, 3.3, 4.1)?

Question

What is the distance between (4.5, 2.6, 3.3, 4.1) and (4, 3, 2, 1)?

Dot Product:

[dot(a,b) = a_1b_1 + a_2b_2 +dots + a_nb_n onumber ]

Do This

Review Sections 1.4 and 1.5 of the Boyd and Vandenberghe text and answer the questions below.

Question

What is the dot product between (u=[1,7,9,11]) and (v=[7,1,2,2]) (Store the information in a variable calleduv)?

Question

What is the norm of vector (u) defined above (store this value in a variabled calledn)?

Question

What is the distance between points (u) and (v) defined above. (put your answer in a variable namedd)


Watch the video: Einheitsvektor, Vektorgeometrie, Vektor mit der Länge 1. Mathe by Daniel Jung (December 2021).