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How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
1 For the two vectors find the scalar product AB and the vector product?
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
What is the angle between 2 vectors when their sum is maximum?
180 degrees* * * * *The exact opposite!Maximum = 0 degrees, minimum = 180 degrees.
The resultant between 2 vectors can be found by placing the vectors?
ma0!
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
