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The cross product a × b (vertical, in purple) changes as the angle between the vectors a (blue) and b (red) changes. The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖a‖‖b‖ when they are orthogonal.


In my opinion, in a cross-product, more emphasis needs to be placed on the oriented-parallelogram formed from the given pair of vectors [with their tails together, or with the second placed at the tip of the first]. The magnitude of the cross-product is the magnitude of the parallelogram's area.


We should note that the cross product requires both of the vectors to be three dimensional vectors. Also, before getting into how to compute these we should point out a major difference between dot products and cross products. The result of a dot product is a number and the result of a cross product is a vector! Be careful not to confuse the two.


First, the cross product isn’t associative: order matters. Next, remember what the cross product is doing: finding orthogonal vectors. If any two components are parallel ($\vec{a}$ parallel to $\vec{b}$) then there are no dimensions pushing on each other, and the cross product is zero (which carries through to $0 \times \vec{c}$).


Cross Product. A vector has magnitude (how long it is) and direction:. Two vectors can be multiplied using the "Cross Product" (also see Dot Product). The Cross Product a × b of two vectors is another vector that is at right angles to both:. And it all happens in 3 dimensions! The magnitude (length) of the cross product equals the area of a parallelogram with vectors a and b for sides:


There are two ways to take the product of a pair of vectors. One of these methods of multiplication is the cross product, which is the subject of this page.The other multiplication is the dot product, which we discuss on another page.. The cross product is defined only for three-dimensional vectors.


The answers about using the cross product are correct, but needlessly complicated. If two vectors are parallel, then one of them will be a multiple of the other. So divide each one by its magnitude to get a unit vector. If they're parallel, the t...


Learn how to determine if two vectors are orthogonal, parallel or neither. You can setermine whether two vectors are parallel, orthogonal, or neither uxsing the dot/cross product or using the ...


The dot product of two parallel vectors is equal to the algebraic multiplication of the magnitudes of both vectors. If the two vectors are in the same direction, then the dot product is positive. If they are in the opposite direction, then the dot product is negative.


They are parallel if and only if they are different by a factor i.e. (1,3) and (-2,-6). The dot product will be 0 for perpendicular vectors i.e. they cross at exactly 90 degrees. When you calculate the dot product and your answer is non-zero it just means the two vectors are not perpendicular.