Use a software program or a graphing utility with vector capabilities to find the lengths of u and v, a unit vector in the direction of v, a unit vector in the direction opposite that of u, u- v, u· u, and v. v. (Round your answers to decimal places.) - (0 1, v7), v-(-1, v7, -1) (a) the norms of u and v |u||- 2.82843 Iv||- 3 (b) a unit vector in the direction of v (c) a unit vector in the direction opposite that of u (d) u.V (e) u.u 8 (f) v.v 9

Q: Let ->u = (2, 1, -1) and ->v = (0, 2, 3). Find the projection of ->u onto ->v and the unit vector…

A: Solve using the concept of vectors.

Q: Define the cross product (vector product) of two vectors. Which algebraic laws are satisfied by…

A: Cross product of vectors a and b is vector c which is perpendicular to both and b , with direction…

Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

A:

Q: Find a unit vector in the direction of v = (-2, 8, 6). %3D

A:

Q: Find a unit vector u in the direction of v. Verify that ||u|| = 1. v = (-6, 6)

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector that has the same direction as the given vector.

A:

Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

A:

Q: ind a unit vector with positive first coordinate that is orthogonal to the plane through the points

A: Given that the plane passes through the points, P(4,1,-1) Q(5,2,0) R(5,2,5)

Q: Use a software program or a graphing utility with vector capabilities to find the lengths of u and…

A: Given: u=0,14,13 , v=2,12,23

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a vector v perpendicular to the vector \mbu= v=

A: Let us consider vector   v⇀=a,b is perpendicular to the vector u⇀=2,2, then ⇒ v→.u→ =0 ⇒2a+2b=0⇒…

Q: Exercise 5. Suppose v is a nonzero vector. Show that any vector w can be written as w = av+ u where…

A: This is a problem of vector space, vector algebra.

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Find the distance from the point P(-3, 1,4) to the line through A(1, 1, 0) and B(-2, 3,-4).

Q: Find a unit vector in the direction of u and in the direction opposite that of u. u-(-7, 24) (a) in…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector that is anti-parallel to the vector (1,2,0,3).

A: A vector is a quantity that has both magnitude, as well as direction. A vector that has a magnitude…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector that is orthogonal to both u and v. u - (5, -1, 3) v = (1, 0, -2) %3D

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Distance = 4.41

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

A:

Q: Use the graph to determine mentally the projection of u onto v. (The coordinates of the terminal…

A: Solve the following

Q: Find a unit vector orthogonal to both a and b, where a = (-1,0, 3) and b = (0, –1,0). Give . an…

A:

Q: A plane passes through the points A, B and C with coordinates (9,1, –4), (13, —4, 7) and (4, 2, −5)…

A: For the given points on the plane the cross product AB→ ×AC → = -6i-51j-21k or can be written as…

Q: Use a software program or a graphing utility with vector capabilities to find the lengths of u and…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find the length of the vector x = [-2, 2, 6 ]

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: The vertices of a triangle in space are (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). Explain how to…

A: Given:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: We need to find distance.

Q: Find a unit vector u in the direction opposite of (-9, –2, –3). u =

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find a unit vector orthogonal to both u and v. u = (-4, 5, -2) v = (-1, 1, 0)

A: The vector which is orthogonal to both u and v is defined as u×vu×v. Here, u=-4,5,-2 and v=-1,1,0.…

Q: Find the length of the vector. v = (5, 0, 3, -2) %3D ||v|| = %3D

A:

Q: Determine whether u and v are orthogonal vectors. 1. u = (6,1, 4), v = (2, 0, -3) 2. u= (0, 0, -1),…

A: Two vectors a and b are orthogonal if a.b = 0 1.) Given u = (6 , 1 , 4)v = (2 , 0 , -3) Then u.v =…

Q: 1. Find all unit vectors that are parallel to the line going through the points (1, 3, – 1) and (2,…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: Find unit vector parallel to u = (2, -3, 2)

A: A unit vector a^ parallel to the vector a⇀ is given by, a^=a⇀a⇀ Where a⇀ is the magnitude of the…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: