Rewrite our vectors in terms of coordinates:
(a1, a2, a3, a4, a5) = (2, 4, 6, 8, 10)(b1, b2, b3, b4, b5) = (1, 3, 5, 7, 9)
Add the respective vector components:
A + B = (a1 + b1 , a2 + b2 , a3 + b3 , a4 + b4 , a5 + b5 )A + B = (2 + 1, 4 + 3, 6 + 5, 8 + 7, 10 + 9)
A + B = (3, 7, 11, 15, 19)
Expresed in vector format, we have:
| 3 |
| 7 |
| 11 |
| 15 |
| 19 |
Rewrite the vector in terms of coordinates:
(a + b1, a + b2, a + b3, a + b4, a + b5) = (3, 7, 11, 15, 19)The formula for this is below:
||A + B|| = Square Root(a + b12 + a + b22 + a + b32 + a + b42 + a + b52)||A + B|| = Square Root(32 + 72 + 112 + 152 + 192)
||A + B|| = √9 + 49 + 121 + 225 + 361
||A + B|| = √765
||A + B|| = 27.658633371879
Common Core State Standards In This Lesson
HSN.VM.B.4, HSN.VM.B.4.C, HSN.VM.B.5, HSN.VM.B.5.A, HSN.VM.B.5.B
How does the Vectors Calculator work?
Free Vectors Calculator - Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
This calculator has 1 input.
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.
This calculator has 1 input.
What 1 formula is used for the Vectors Calculator?
||A|| = Square Root(a12 + a22 + a32)
What 14 concepts are covered in the Vectors Calculator?
- angle
- the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
- cauchy schwarz inequality
- the lengths of the dot product of vectors is less than or equal to the product of the lengths of the vectors
- cosine
- cos(θ) is the ratio of the opposite side to the hypotenuse.
- direction
- the line or course on which something is going
- distance
- interval between two points in time
d = rt - inequality
- a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
>, <, ≤, ≥ - length
- the measurement or extent of something from end to end
- magnitude
- the size, extent, or importance of something
- orthogonal
- Two perpendicular lines - two lines forming a 90 degree angle
- orthogonal
- Two perpendicular lines - two lines forming a 90 degree angle
- perpendicular
- two lines which intersect to form a right angle
- product
- The answer when two or more values are multiplied together
- projection
- the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines.
- vector
- directed line segment
