1. Given the following vectors: u=(1, 2, -4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle between u and v e) unit vector 2. Suppose that B =(2, 2, 1) and makes 30⁰ with A and AB= 6. What is the magnitude of A?

Q: ude 5. Find the area of the triangle created by the

A: Given a, b and c are three vectors with the same magnitude 5.

Q: 4. A|-2,5 А = 2, B = 3 and the angle formed by A and B is 120°. Determine the unit vector in the…

A: Solving

Q: Determine the resultant of two vectors with magnitudes of 50 and 30 and an angle of 110 degrees…

A: let  A=50 & B=30, θ=1100 We know resultant between two vectors A→ & B→ when angle between…

Q: Suppose that B=(2, 2, 1) and makes 30⁰ with A and AB=6. What is the magnitude of A?

A: Vectors are the mathematical quantity which obeys the set of axioms. In general, vectors are…

Q: 23. Find the angle between the vectors u = [-9,1, 3] and = [0,2,-5].

A:

Q: 3) What measure of the angle formed by the vectors u = (9,5,-3) and v = (-8,0,3)? Give your answer…

A: To find the measure of the angle formed by the vectors .

Q: Determine for the three vectors: x = ai+bj+ck, y = 2i+k and z = di+ej+fk where a = 2, b = -3, c = 3,…

A:

Q: Determine the angle between the following vectors a) u = (1, 1) & v = (1 – V3, v3+1) b) u = (a, b) &…

A: The dot product of two vector a→ and b→ is given by the equation ; a→·b→=|a→||b→| cos θ where θ is…

Q: Let A = (4, –4,4, 0) and B = (-4,3, –4, 1) be points in R*

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: In the adjoining figure ū and V are unit vectors. Evaluate the following and input your numerical…

A:

Q: 1. Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find: a) u.v b) u.u c) (u.v) v d) angle…

A:

Q: 2. Find the exact angle between vectors a = 3 î - j - 2k – 18 10 b = v – w, wherev = 2î + ĵ + 4kandŵ…

A:

Q: 5. Determine the resultant of two vectors with magnitudes of 30 and 70 units and an angle of 45…

A:

Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

A:

Q: Let u = -3) and v=(5, -2) and w= = (-6, -4). Fin (2, -3)

A: Givenu=2,-3,v=(5,-2),w=(-6,-4) The objective is to find the angle between the vectors 6) angle…

Q: 1. Three vectors are given by: å = 2î – 3ĵ + 5k, b = -2î + 7j – k and č = lî + 2j – 4k. axb Find a,…

A:

Q: 3. Given (3, 10,-8) and v = (-1,6,4), b) find a unit vector in the same direction as v-u

A: The given problem is to find the unit vector in the same direction of the vector v-u. Given vectors…

Q: Assume b = i +3+k What is the angle that vector 6 makes with z axis (with k unit vector)? Report the…

A: Given vector b→=i^+j^+k^ let a→=k^ We have to find the angle between b→=i^+j^+k^ and a→=k^

Q: 4. Which vector(s) below is perpendicular to ū = 2i– 3j? A. V = 27+ 25 B. W = 31+ 25 C. Ã = 5ï – 75…

A: Given: The vector U→=2i→-3j→, To determine: Which of the following vectors are parallel to the given…

Q: Suppose that the magnitude of vector u = 5 and the magnitude of vector v=7 and the dot product of u…

A:

Q: Which of the following vectors represent a + b, if a and b are given as below? b a a) b) c)

A: Given : Vector a and vector b is given

Q: If au + bû = 0, where a and b are positive. If a = -b, what must be true of vectors ū and v? Explain…

A: The relation between a and b is a=-b. Also, the relation between vectors u⇀ and v⇀ is au⇀+bv⇀=0⇀.

Q: Q.1) Choose the correct answer for the following: (choose 5 only) 1- The vector from point P=(2,2,1)…

A: This question can be solved using the concept of vectors.

Q: 5. Determine if u and v are orthogonal u = (cos, sin 0,-1); v = (sin 0.- cos 0,0)

A:

Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: 4. For the vectors (2, 1) and = (1, 2) Find the dot product u · v, and the angle 0 between the two…

A: According to the given information, it is required to calculate the dot product and angle between…

Q: and AB= 6. What is the magnitude of A? . What is the angle between A and B if A.B=0

A:

Q: 1. Given vectors ū(-3,2,6) and (4,1,5) determine the angle between ū and v

A:

Q: 13. The angle between the vectors and .

A:

Q: 1) Given two vectors as A = 2â, + 2â, -â, at point (3,60°,180°) and B =-2â, + 4â, - 4â, at point…

A: Consider the given vectors:

Q: Find the given vector. Vector v = (x, y) of length 18 making an angle of 30° with the x-xis. (Use…

A: