Given two vectors A = 3.80 i^ + 7.00 j^ and B = 5.10i^ − 2.20j^, find the scalar product of the two vectors A→ and B→, and the angle between them.

Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.

Use the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.

Given two vectors A⃗ = 4.20 i^+ 7.60 j^ and B⃗ = 5.70 i^− 2.40 j^ , find the scalar product of the two vectors A⃗  and B⃗ .   Find the angle between these two vectors.

For the pair of vectors A = (6.00î + 4.00ĵ) and B = (9.0oî – 6.00ĵ) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) %3D (a) The scalar product A: B = (b) The angle 0 between the vectors (c) The angles a and ß which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = %D (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes Y 8 %3D

With the given three vector A, B, C. Determine the magnitude of the dot product of vectors AxC and CxB A= 2i - 3j + 4k B= -3i - 6j + 5k C= 4i + 2j

For the pair of vectors A = (6.00î + 4.00j) and B = (9.00î – 6.00j) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) (a) The scalar product A·B = (b) The angle 0 between the vectors (c) The angles a and B which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = B = (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes 8 =

Given the points M(0.1, -0.2, -0.1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector RMN; (b)the dot product RMN. RMP ; (c) the scalar projection of RMN on RMP; (d) the vector projection of RMN on RMP; (e) the angle between RMN on RMP.

Consider two vectors F = – 2i + 3j – k, and S = 4i – 3j + 2k. The dot product F.S =

Problem 20:  Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2. In this problem, you must assume that both components of B are positive, Bx > 0, and By > 0. Part (a)  If the scalar product of these two vectors is A⋅B = 16.3, what is the x-component of the vector B? You may assume that Bx > 0. Part (b)  What is the y-component of the vector B? Again, assume By > 0.