Consider the vectors a = 3i - 4 +2k , 6* = 2i + k and c =-j+3k* . Find: a) The angle between a and b b) A vector perpendicular to both a and b +c c) the projection of c onto b -a

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: Determine the two unit vectors that are orthogonal to v = (1,2). Which two unit vectors are parallel…

A: Let the required unit vector orthogonal to v be <x,y>

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is

A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…

Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

A:

Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

A:

Q: Find a unit vector that has the same direction as the given vector. 4i - j+ 8k

A: Unit vector means the vector whose magnitude is equal to one. So to find the unit vector in the…

Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2). b= (0,…

A: The volume Parallelepiped by the vector a, b and c is given as:

Q: ) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpe ular to CD, and…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: ors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are mutuallyperpendicular unit vectors…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

A:

Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: Which two vectors are perpendicular to both a and b?

A:

Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Express the vector in the form (a, b). 1(i + j) ji + jl

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Find a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c.  a = 1, 2, 2, b = −1,…

A:

Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

Q: Find the vector of length v7 in the direction of AB + AC

A:

Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Derive the relation between unit Vectors of Glindrical and Cartesian Coordinates?

A:

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

A:

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 2, 3), b = (-1,…

A: Given vectors:                        a=1, 2 , 3, b= -1, 1, 4, c=5, 1, 5

Q: Write four forms of dot product for two vectors A and B by defining their metric tensor?

A: The dot product of two vectors, A and B in metric tensor form can be written as A→·B→=gμν aνbμ ,…

Q: Find the angle between the vectors u (2, –1) and v = (1, 1).

A:

Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: The position vectors of A and B with respect to the origin O are a and b respectively. M is the…

A: Given that position vector of A and B with respect to the origin O are a and b respectively. M is…

Q: Prove the stated property of distance between vectors.d(u, w) < d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 3, 3), b = (-1,…

A:

Q: Check whether u = 6i – 2j+k and v= -4i – 3j+9k are parallel or not. Then, find the area of triangle…

A:

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1.3,4). b =…

A:

Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Show that a unit vector in the plane can be expressed as u = (cos u)i + (sin u)j, obtained by…

A: To show that a unit vector can be expressed as u = (cos u) i + (sin u) j.

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: Express the vector v = 4i + 2j - k in terms of magnitude and %3D direction.

A: