To find
u +
v , we first draw the vector
u , and from the terminal end of
u , we drawn the vector
v . In other words, we have the initial point of
v meet the terminal end of
u . This position corresponds to the notion that we move along the first vector and then, from its terminal point, we move along the second vector. The sum
u +
v is the resultant vector because it results from addition or subtraction of two vectors. The resultant vector travels directly from the beginning of
u to the end of
v in a straight path, as shown in
[link] .
Vector subtraction is similar to vector addition. To find
u −
v , view it as
u + (−
v ). Adding −
v is reversing direction of
v and adding it to the end of
u . The new vector begins at the start of
u and stops at the end point of −
v . See
[link] for a visual that compares vector addition and vector subtraction using
parallelograms .
Adding and subtracting vectors
Given
$u$$=\u27e83,-2\u27e9$ and
$v$$=\u27e8\mathrm{-1},4\u27e9,$ find two new vectors
u +
v , and
u −
v .
To find the sum of two vectors, we add the components. Thus,
To find the difference of two vectors, add the negative components of
$\text{\hspace{0.17em}}v\text{\hspace{0.17em}}$ to
$\text{\hspace{0.17em}}u.\text{\hspace{0.17em}}$ Thus,
While adding and subtracting vectors gives us a new vector with a different magnitude and direction, the process of multiplying a vector by a
scalar , a constant, changes only the magnitude of the vector or the length of the line. Scalar multiplication has no effect on the direction unless the scalar is negative, in which case the direction of the resulting vector is opposite the direction of the original vector.
Scalar multiplication
Scalar multiplication involves the product of a vector and a scalar. Each component of the vector is multiplied by the scalar. Thus, to multiply
$v$$=\u27e8a,b\u27e9$ by
$k$ , we have
$$kv=\u27e8ka,kb\u27e9$$
Only the magnitude changes, unless
$\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is negative, and then the vector reverses direction.
Performing scalar multiplication
Given vector
$\text{\hspace{0.17em}}v$$=\u27e83,1\u27e9,\text{\hspace{0.17em}}$ find 3
v ,
$\frac{1}{2}$$v,\text{\hspace{0.17em}}$ and −
v .
See
[link] for a geometric interpretation. If
$\text{\hspace{0.17em}}v$$=\u27e83,1\u27e9,$ then
In some applications involving vectors, it is helpful for us to be able to break a vector down into its components. Vectors are comprised of two components: the horizontal component is the
$\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ direction, and the vertical component is the
$\text{\hspace{0.17em}}y\text{\hspace{0.17em}}$ direction. For example, we can see in the graph in
[link] that the position vector
$\u27e82,3\u27e9$ comes from adding the vectors
v_{1} and
v_{2} . We have
v_{1} with initial point
$\text{\hspace{0.17em}}\left(0,0\right)\text{\hspace{0.17em}}$ and terminal point
$\text{\hspace{0.17em}}\left(2,0\right).\text{\hspace{0.17em}}$
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
Y
master
X2-2X+8-4X2+12X-20=0
(X2-4X2)+(-2X+12X)+(-20+8)= 0
-3X2+10X-12=0
3X2-10X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20
x2-4x2-2x+12x+8-20
-3x2+10x-12
now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
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explain and give four example of hyperbolic function
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
the Cayley hamilton Theorem state if A is a square matrix and if f(x) is its characterics polynomial then f(x)=0 in another ways evey square matrix is a root of its chatacteristics polynomial.