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  • These aren't locations anymore but ''vectors''. This number is then computed from these two ''vectors'':
    113 KB (19,680 words) - 00:08, 23 February 2019
  • ==The length of vectors, the norm== [[Image:length and angle.jpg|150px|right]]
    21 KB (3,396 words) - 20:31, 10 August 2011
  • We transition to from numbers to ''vectors''. But what are the operations? ...mer. This is very similar to multiplication of numbers; after all they are vectors of dimension $1$... Let's match the two problems and their solutions:
    113 KB (18,750 words) - 02:33, 10 December 2018
  • ...an listen to a conversation at the other focus even if there are obstacles between them. $\square$ ...ppens when the ''angular velocity'' is constant: the object turns the same angle per unit of time:
    130 KB (22,842 words) - 13:52, 24 November 2018
  • '''Exercise.''' What is the relation, if any, between these two pairs of properties: (a) even and one-to-one, (b) odd and one-to- Now, we know that the axis of a parabola lies half-way between the two $x$-intercepts. Therefore, it is:
    143 KB (24,052 words) - 13:11, 23 February 2019
  • Now, if the vectors represent velocities of particles, what kind of flow is this? This isn't a Now, if the vectors represent velocities of particles, what kind of flow is this? It looks like
    74 KB (13,039 words) - 14:05, 24 November 2018
  • The equations mean that the vectors of the vector field are tangent to these trajectories. ODEs are discussed i ...apter 21 that ''Newton's Law of Gravity'' states that the force of gravity between two objects is given by the formula:
    91 KB (16,253 words) - 04:52, 9 January 2019
  • *the difference between the two: $x_n-p_n$ and $y_n-q_n$, which is the direction from the hound tow *the unit vector in this direction (dividing by the distance between them);
    50 KB (8,692 words) - 14:29, 24 November 2018
  • Of course, it is sufficient to know the sign of the derivative to distinguish between increasing and decreasing behavior. Therefore, this behavior depends only o ...eveloping, the sign of the exterior derivative will tell us the difference between increasing and decreasing behavior. But the derivative only uses the topolo
    42 KB (7,131 words) - 17:31, 30 November 2015
  • ...''' only, until now. By that I mean that we did a lot of computations with vectors. The distance between $a=(a_1,\ldots,a_n)$ and $b=(b_1,\ldots,b_n)$ is
    14 KB (2,404 words) - 15:04, 13 October 2011
  • *the lengths of vectors and *the angles between vectors. $\\$
    35 KB (5,871 words) - 22:43, 7 April 2016
  • When a ball is thrown in the air under an angle, it moves in both vertical and horizontal directions, simultaneously and in The ''path'' of the ball will appear to an observer -- from the right angle -- as a curve. It is placed in the $xy$-plane positioned vertically:
    76 KB (13,017 words) - 20:26, 23 February 2019
  • ...is is very similar to multiplication of numbers; after all they are column-vectors in dimension $1$... Let's align the two problems: In other words, we need to find a way to stretch these two vectors so that the resulting combination is the vector on the right:
    46 KB (7,625 words) - 13:08, 26 February 2018
  • ...ling'': the rate of cooling of an object is proportional to the difference between its temperature and the ambient temperature. To sum up, the amount of heat exchanged between two rooms is proportional to:
    39 KB (6,850 words) - 15:29, 17 July 2015
  • *Find the plane through the point $P=(-1,6,-5)$ and parallel to the vectors $A=<1,1,0>$ and $B=<0,1,1>.$ *Vectors $A$ and $B$ are given below. Copy the picture and illustrate graphically (a
    46 KB (8,035 words) - 13:50, 15 March 2018
  • <!--s-->[[image:algebra of vectors.png|center]] *For every two vectors, what is their sum?
    13 KB (2,233 words) - 14:41, 20 February 2015
  • ...of the vector $N$ is revealed once we remember that the dot product of two vectors is $0$ if and only if they are perpendicular. [[image:plane as perpendicular vectors.png| center]]
    97 KB (17,654 words) - 13:59, 24 November 2018
  • Setting aside possible connections between the integrands, the pattern of the ''domains of integration'' is clear. The ...ion between $R$ and $\partial R$ is a matter of ''topology''. The relation between $d \omega$ and $\omega$ is a matter of ''calculus'', the calculus of differ
    34 KB (5,619 words) - 16:00, 30 November 2015
  • The distance between $a=(a_1,\ldots,a_n)$ and $b=(b_1,\ldots,b_n)$ is But does the angle between two vectors even make sense in ${\bf R}^n$?
    32 KB (5,426 words) - 21:57, 5 August 2016
  • The distance between $a=(a_1,\ldots,a_n)$ and $b=(b_1,\ldots,b_n)$ is We can measure vectors and, therefore, can consider [[convergence]]:
    2 KB (410 words) - 15:09, 9 June 2012

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