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Why you are using cosine function in dot product of two vectors?
Wiki User
∙ 13y ago
It comes from the Law of Cosines.
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For any two vectors A and B, the projection of A onto B, that is, the component of A along B, is ab.cos(x) where x is the angle between the two vectors. By symmetry, this is also the projectoin of B onto A.
Wiki User
∙ 13y ago
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How angle between two vectors is found using cross product?
A x B = |A| |B| sin[theta]
What is defined as force times distance?
Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).
What is the vector triangle?
The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)
What is difference of using sine to cosine and tangent?
They are different trigonometric functions!
How do you add vectors using the component method?
1) Separate the vectors into components (if they are not already expressed as components). 2) Add each of the components separately. 3) If required, convert the vectors back to some other form. For twodimensional vectors, that would polar form.
How do you do rotation in math?
A vector rotation in math is done on a coordinate plane.2D vectors can be rotated using the cross and dot product.3D vectors are rotated using matrix based quaternion math.
How angle between two vectors is found using cross product?
A x B = |A| |B| sin[theta]
What are sine and cosine functions?
Sine allows us to find out what a third side or an angle is using the equation sin(x) = opposite over hypotenuse (x being the angle). Cosine has the same function but instead uses the equation cosine(x)= opposite over adjacent
What should be the angle between 2 vectors a?
The angle between two vectors a and b can be found using the dot product formula: a · b = |a| |b| cos(theta), where theta is the angle between the two vectors. Rearranging the formula, we can solve for theta: theta = arccos((a · b) / (|a| |b|)).
What are the different methods in adding vectors?
Vectors can be added using the component method, where you add the corresponding components of the vectors to get the resultant vector. You can also add vectors using the graphical method, where you draw the vectors as arrows and then add them tip-to-tail to find the resultant vector. Additionally, vectors can be added using the trigonometric method, where you use trigonometry to find the magnitude and direction of the resultant vector.
What is defined as force times distance?
Work is defined as the dot product of force times distance, or W = F * d = Fd cos (theta) where theta is the angle in between the force and distance vectors (if you are doing two dimensions). In three dimensions, use the standard definition for the dot product (using the component form of the vectors).
What is the angle between unit vectors i plus j and j plus k?
The angle between two vectors can be found using the dot product formula: A · B = |A| |B| cos(theta). In this case, the dot product of the two given unit vectors is (1)(0) + (1)(1) + (0)(1) = 1. The magnitudes of the vectors are √2 and √2, therefore cos(theta) = 1 / (2)(2) = 1/4, giving theta = arccos(1/4) ≈ 75.5 degrees.
Resultant velocity is calculated using which two math functions?
The resultant velocity can be calculated using vector addition, which involves adding the velocities of the object in both the x- and y-direction. This is typically done using trigonometric functions like sine and cosine to determine the direction and magnitude of the resultant velocity.
Cross product is not difine in two space why?
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.
What is the vector triangle?
The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)
What is difference of using sine to cosine and tangent?
They are different trigonometric functions!
What is the shortcut to using the product rule?
manipulate the function algebraically, so that the result is easier to differentiate
