1) Determine the angle between vectors: U = <2, -3, 4> and V= <-1, 3, -2>...

1) Determine the angle between vectors:

U = <2, -3, 4> and V= <-1, 3, -2>

2) determine the distance between line and point

P: -2x+3y-4z =2

L: 3x – 5y+z =1

3) Determine the distance between the line L and the point A given by

L; (x-1)/2 = (y+2)/5 = (z-3)/4 and A (1, -1,1)

4) Find an equation of the line given by the points A, B and C.

A (2, -1,0), B (-2,4,-1) and C ( 3,-4,1)

5) Determine whether the lines are parallel, perpendicular or neither.

(x-1)/2 = (y+2)/5 = (z-3)/4 and (x-2)/4 = (y-1)/3 = (z-2)/6

6) A) Find the line intersection of vector planes given by the equations

-2x+3y-z+4=0 and 3x-2y+z=-2

B) Given U = <2, -3, 4> and V= <-1, 3, -2>

Find

a. U . V

b. U x V

7) Find the angle between the planes:

3x -5y+7z -4=0 and 3x -2y+5z +3 =0

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7}

Calculate the angle between the vectors u = {5, -2, 3} and v ={4,-5,7} give details.

1. a. Determine the angle (in radians) between the vectors 〈4, −5, 6〉 and 〈−2, 2,...

1. a. Determine the angle (in radians) between the vectors 〈4, −5, 6〉 and 〈−2, 2, 3〉. b. Find the vector projection of 〈1, 2, 4〉 onto 〈1, 1, 1〉. c. Compute the cross product 〈2, 3, 4〉 × 〈1, 0, −1〉.

for u=<2,1,-3> and v=<1,0,2>, a) find the angle between u and v b) use the formula...

for u=<2,1,-3> and v=<1,0,2>, a) find the angle between u and v b) use the formula proj_a b=((a•b)/|b|^2)b to find vector projection of v onto u c) sketch vectors u, v, and the projection found with only using arrows d) find the area of the parallelogram determined by u and v

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ =...

Suppose u, and v are vectors in R m, such that ∥u∥ = 1, ∥v∥ = 4, ∥u + v∥ = 5. Find the inner product 〈u, v〉. Suppose {a1, · · · ak} are orthonormal vectors in R m. Show that {a1, · · · ak} is a linearly independent set.

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give...

show that for any two vectors u and v in an inner product space ||u+v||^2+||u-v||^2=2(||u||^2+||v||^2) give a geometric interpretation of this result fot he vector space R^2

For the following exercises, calculate u ⋅ v. Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.

For the following exercises, calculate u ⋅ v.Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.

1. For this question, we define the following vectors: u = (1, 2), v = (−2,...

1. For this question, we define the following vectors: u = (1, 2), v = (−2, 3). (a) Sketch following vectors on the same set of axes. Make sure to label your axes with a scale. i. 2u ii. −v iii. u + 2v iv. A unit vector which is parallel to v (b) Let w be the vector satisfying u + v + w = 0 (0 is the zero vector). Draw a diagram showing the geometric relationship between...

Suppose that vectors x and y are such that IxI=3 and IyI=4, and the angle between...

Suppose that vectors x and y are such that IxI=3 and IyI=4, and the angle between x and y is 71°. Solve the triangle determined by the vectors 3x , y, and I3x - y I. That is, report all side lengths and angles in this triangle to 3 decimal places accuracy.

For the following exercises, calculate u ⋅ v. Given v = 〈−3, 4〉 draw v, 2v, and 1/2 v.

For the following exercises, calculate u ⋅ v.Given v = 〈−3, 4⟩ draw v, 2v, and 1/2 v.

Find the angle θ between the vectors in radians and in degrees. u = cos π...

Find the angle θ between the vectors in radians and in degrees. u = cos π 3 i + sin π 3 j, v = cos 3π 4 i + sin 3π 4 j (a) radians (b) degrees

Subjects