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Cross products and dot products are two operations that can be done on a pair of 2-dimensional, 3-dimensional, or n-dimensional vectors. Both can be viewed in terms of mathematics or their physical representations.
The dot product of two three-dimensional vectors A=
The cross product is a little more complicated. In three dimensions, A × B = <a2b3 − a3b2, a3b1 − a1b3, a1b2 − a2b1>. Notice that this operation results in another vector. This vector always points in a direction perpendicular to both A and B, and this direction can be determined by the right-hand rule. Physically, the magnitude of this vector equals |A|*|B|sinθ, or the magnitude of the first vector times the component of the other that is perpendicular to the first. So the cross product is 0 when the vectors are parallel.
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What compound words start with cross?
crossway crossroads crosswalk crosshair crossproduct crossword crossbreed crossover
What are compound words starting with cross?
crossway crossroads crosswalk crosshair crossproduct crossword crossbreed crossover
If all the components of the vectors A1 and A2 were reversed.how would this alter A1 and A2?
V1XV2 their crossproduct will be in one direction and the V2xV1 direction will be oppsite. For example. V1 is going right and V2 is going left, their v1xV2 will be going towards you (arrow coming at you). And V2xV1 direction will be going away from you (you shooting arrow at target).
Can dotproduct of two vectors be negative?
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
How are poportion and crossproduct the same?
PoportionA poportion is ----- = ----- (line equals line) for example: 3 X---- = ---- your equation is X12= 23 x 3 (you ALWAYS solve for X)12 23 X= 69 (divided) 12X= 5.75you always do your criss cross and then times them togetherCross Productswhen you have a two fractions you always want to cross them like and "X" then if they are the same answers the are porpotional.they are the same because you have to cross them together and multiply them
Would you show an example of math how to find the cross product?
For two vectors (A & B) in 3-space, using the (i j k) unit vector notation:if A = a1*i + a2*j + a3*k, and B = b1*i + b2*j + b3*k the cross product A X B can be found by computing a determinant of the following matrix:| i j k ||a1 a2 a3 ||b1 b2 b3 |Mathematically, it will look like this: (a2*b3 - a3*b2)*i- (a1*b3 - a3*b1)*j + (a1*b2 - a2*b1)*kI did do just a little copy/paste from the crossproduct website, which I've posted a link to, which has some good information.
What is the power if a force is applied on a body and it moves with a velocity V?
P=v/f=======================Well, let's see.Force = newtonWork = force x distance = newton-meterPower = work/time = (newton-meter)/(second)The first answer above says Power = (Velocity)/(force). Let's check it out.Speed= length/time = meter/secondForce = newtonV/f = (meter)/(newton-second)Power = (newton-meter)/(second)We don't know what kind of monstrosity V/f is, but it's not power.How about (force) x (speed) = (newton) x (meter/second) = (newton-meter)/(second).That's a lot nicer.In all its glory, Power = F · V .You, the questioner, said 'velocity', not 'speed', so you're going to have toface this for what it is ... the product of two vectors. Force is a vector, andso is velocity, but power is not. The way you multiply two vectors and geta scalar is by means of the 'vector dot-product'. The dot-product of forceand velocity is:(magnitude of the force) times (magnitude of the velocity) times (cosine of the angle between them).The reason for this is: If the force isn't pushing in the same direction as the velocity,then not all of it produces power, only the part of it that points in the right direction.If you're trying to push a heavy wagon and it's not moving fast enough, whatdo you do ? You let your feet get farther behind the wagon, and you crouchdown so that your shoulders are lower and more in line with the wagon. Thereason you do that is: Only the part of the force that lines up with the motionhelps with the motion, so if you want to push faster, you get the force down towhere it lines up better with the motion. You reduce the angle between theforce and the motion. That makes the cosine of the angle greater, so the dotproduct is greater. Even though the magnitude of the force hasn't changed,the component of the force in the direction where you need it has becomegreater, by reducing the angle between them.
