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Why you use cos angle with dot product and sin angle with cross product?
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What are the applications of cross product and dot product?
Cross product tests for parallelism and Dot product tests for perpendicularity. Cross and Dot products are used in applications involving angles between vectors. For example given two vectors A and B; The parallel product is AxB= |AB|sin(AB). If AXB=|AB|sin(AB)=0 then Angle (AB) is an even multiple of 90 degrees. This is considered a parallel condition. Cross product tests for parallelism. The perpendicular product is A.B= -|AB|cos(AB) If A.B = -|AB|cos(AB) = 0 then Angle (AB) is an odd multiple of 90 degrees. This is considered a perpendicular condition. Dot product tests for perpendicular.
When does the magnitude of dot product and cross product of vectors is equal?
If x is the angle between the two vectors then the magnitudes are equal if cos(x) = sin(x). That is, when x = pi/4 radians.
Why you use cosine theta with cross product?
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
What is the difference between a 'dot product' and a 'cross product'?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.a X b= ║a║║b║sin(θ)n
Why we use sine angle in cross product while cos angle in dot product?
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
What are the applications of cross product and dot product?
Cross product tests for parallelism and Dot product tests for perpendicularity. Cross and Dot products are used in applications involving angles between vectors. For example given two vectors A and B; The parallel product is AxB= |AB|sin(AB). If AXB=|AB|sin(AB)=0 then Angle (AB) is an even multiple of 90 degrees. This is considered a parallel condition. Cross product tests for parallelism. The perpendicular product is A.B= -|AB|cos(AB) If A.B = -|AB|cos(AB) = 0 then Angle (AB) is an odd multiple of 90 degrees. This is considered a perpendicular condition. Dot product tests for perpendicular.
When does the magnitude of dot product and cross product of vectors is equal?
If x is the angle between the two vectors then the magnitudes are equal if cos(x) = sin(x). That is, when x = pi/4 radians.
When cross and dot product equal what is angle between A and B?
A · B = |A| |B| cos(Θ)A x B = |A| |B| sin(Θ)If [ A · B = A x B ] then cos(Θ) = sin(Θ).Θ = 45°
Why you use cosine theta with cross product?
Normally you use sine theta with the cross product and cos theta with the vector product, so that the cross product of parallel vectors is zero while the dot product of vectors at right angles is zero.
Why in dot product you use cos and in vector product sin?
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
What is the difference between the ''dot product'' and the ''cross product''?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and b define.a X b = ║a║║b║sin(θ)n
What is the difference between a 'dot product' and a 'cross product'?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.a X b= ║a║║b║sin(θ)n
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
What are the applications of cross product and dot product in physics?
cross: torque dot: work
How do you find the dot product ab of two vectors if you know their lengths and the angle between them?
<ab> = |a|*|b|*cos(x) where |a| is the length of the vector a, |b| is the length of the vector b, and x is the angle between them.
What is vector dot product?
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
