In Exercises 57-62, compute the angle between the two planes, defined asthe angle 0 (between O and n) between their normal vectors (Figure 10).60. x - 3y + z = 3 and 2x - 3z = 4

Q: 6. What is the measure of the angle 0 between the vectors u : = (6, 2, 1) and 7 = (−4, 1, 2)?

A:

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: Find the vector with length 3 making an angle of 7π/4 with the positive x-axis.

A: Given that the vector with length of 3 makes an angle of 7π/4 with the positive x-axis.

Q: In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0…

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

Q: In Exercises 57-62, compute the angle between the two planes, defined asthe angle 0 (between O and…

A: Explanation: To find the angle between two planes, one has to find the angle between normal…

Q: Find the angle θ between the vectors.u = (−4, 3), v = (0, 5), ⟨u, v⟩ = 3u1v1 + u2v2

A: Now,

Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

A:

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

A:

Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

A:

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: Find a vector of length 5 in the direction opposite that of (3, –2, V3).

A: Let the given vector be              a=3i-2j+3k The vector in the direction opposite to a  is  -a.…

Q: Find a vector of length 5 that is orthogonal to both vectors ⟨4,−1,0⟩ and ⟨−3,2,−1⟩

A: The vector orthogonal to two vectors u,v is = ± (u×v)/ |u| |v| Here u =  ⟨4,−1,0⟩ , v =…

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

A:

Q: Find a vector of length 2 orthogonal to the plane 3x – 4z = 5. %3D

A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: This problem is related to core exercise 31 (module 5) in the textbook, and requires you to do some…

A: Given : line l has the vector form           x→=t-11+01 and vector a→ is a→=26 To find : projection…

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Find a unit vector that is orthogonal to both [0, 1, 1] and [1, 0, 1].

A: The given vectors are u=(0,1,1) & v=(1,0,1).

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

A:

Q: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: Find two unit vectors orthogonal to both (1,-1,1) and (1,0,3)

A:

Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

A:

Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

A:

Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

A:

Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

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

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: Compute the cosine of the angle between the plane through P = (6,0,0), Q = (0,7,0), and R = (0,0,5)…

A:

Q: The terminal point of the vector v = i +2j +3k with initial point (4, 2, –3) is

A:

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: 8. Show that the cross product u x v of the vectors u = (-3, 5, -4) and v = (-3, -5, -5) is…

A:

Q: Compute the cosine of the angle between the plane through P – (6,0,0). Q = (0, 5,0), and R = (0,0,9)…

A: (a). Given points are P6,0,0, Q0,5,0 and R0,0,9. We know that equation of plane through a,0,0, 0,b,0…

Q: Find the magnitude of the projection of (- 1, 2) onto the vector (3, 5)

A:

Q: Show thet direcion vectors of Tue Iae メ-3 レ り+ チ一て Laeメ-コ X-3 ソャ) Z-3 -2 are orthogohal

A: Direction vectors and orthogonality

Q: 3. What is the initial point of vector w if the component form is and the terminal point is (4, 1)?

A:

Q: This problem is related to core exercise 31 (module 5) in the textbook, and reguires you to do some…

A:

Q: Let u, = (1,1,1)", u2 = (1,2,2)T and uz = (2,3,4)", find the coordinates of the vectors (2,3,2)" and…

A: Solving by linear combination method

Q: 6. Find a unit vector that is orthogonal to both [0, 1, 1] and [1,0, 1].

A: We will find the unit vector orthogonal to both the vectors as following.

Q: Find a vector a that has the same direction as (-10,7, 10) bưut has length 4.

A: In the given problem we have to find a vector a that has the same direction as -10, 7, 10 but has…

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2

Q: The vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

A: