Question

Versors are unit modulus vectors. They serve to write the equation of other vectors as a function of them. Like vectors, vectors have three different directions in the plane. Determine the vector defined between points A(2,9) and B(-2,6)​

Answer 1

Versors are unit modulus vectors. They serve to write the equation of other vectors as a function of them. Like vectors, vectors have three different directions in the plane. Determine the vector defined between points A(2,9) and B(-2,6)

Answer 2

A unit vector in a normalized vector space is a vector of length 1. A unit vector is often denoted by a lowercase letter with a caret, or "hat". We have the answer:

`\begin{pmatrix} \bold-( \bold4)/( \bold5)& \bold-( \bold3)/( \bold5)\end{pmatrix}`

Vector of a Vector

A vector is a quantity that has magnitude and direction. A vector that has a magnitude of 1 is a unit vector. It is also known as Direction Vector. Learn vectors in detail here.

For example, the vector v = (1,3) is not a unit vector, because its magnitude is not equal to 1, that is, |v| = √(1²+3²) ≠ 1. Any vector can be made a unit vector by dividing it by the magnitude of the given vector.

Let's calculate the vector AB = B-A = (-2, 6) - (2, 9) = (-4, -3)

`\mathrm{ \bold{Calculating\:the\:unit\:vector\:of\:}}\left|\vec{ \bold{a\:}}\right|:\quad \hat{ \bold{a\:}}=\frac{\vec{ \bold{a \:}}}{\left|\vec{ \bold{a\:}}\right|} \:`

`\hat{ \bold{a\:}}= \bold{\frac{\begin{pmatrix} \bold- \bold4& \bold- \bold3\end{pmatrix}}{5}}`

`\begin{pmatrix}-( \bold4)/( \bold5)&-( \bold3)/( \bold5)\end{pmatrix}`