3. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i + j, w = i- 4j OA. Orthogonal B. Neither orthogonal nor parallel C. Not enough information D. Parallel

Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

A:

Q: Which of the following properties will be used when two or more vectors are perpendicular? a. dot…

A:

Q: Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v= 2j. w=…

A:

Q: Find the following for the vectors u = 6i – 5j + 7k and v = - 6i + 5j - 7 k. a. v•u, v|, and u b.…

A:

Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

A:

Q: Find the cross product x . Is the resulting vector perpendicular to the given vectors? O ; yes O ;…

A: Vectors < -1, -3, -8 > and < 7, 4, -5> . To find cross product.

Q: Determine the dot product of vectors a, b when |a| = 5, |b| = 1 and the angle between a and b is…

A:

Q: b) Consider the vectors a = 3i – 2 j +7 K, and b = -5 i +4 j-3 k, find 1- a.b 2- Angle between a and…

A: b Given vectors are a=3i−2j+7k and b=−5i+4j−3k. 1 We have to find the a⋅b…

Q: Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find…

A: Given that the plane Π2 contains the point O, A and B and the plane Π3 contains the points O, A and…

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

A:

Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: Suppose that ac + bd = 0. Show that vectors la, b] and [c, d] are perpendicular. The number ac + bd…

A:

Q: 3) Find the angle between A = 2i + 2j – k and B = 6i – 3j + 2k. 4) Determine the unit vector…

A:

Q: Rewrite the following vectors in term of unit vectors а. ОP %3D (9, -2) b. 0Q = (7,0,8)

A:

Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Compute the dot product of the two given vectors: 27 1 3. Answer:

A:

Q: Consider the vectors u = (2,0) and v = (-4,4). Sketch the vectors, find the angle between the…

A:

Q: Determine the angle between the given vectors. a = 3i – 2j, b = 2i + 2j (b) и %3D (1,—4, 2), v %3D…

A:

Q: In parallelogram ABCD, E is the midpoint of the diagonals. Тext Let AD = ū and AB = v. A D Express…

A: AD⇀=BC⇀=u⇀ AB⇀=DC⇀=v⇀

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+fk where a = 3, b = -3, c =…

A:

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

A:

Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

Q: State whether the vectors are parallel, orthogonal, or neither. v = 2i + j, w = i - 2j O Orthogonal…

A:

Q: Given the two vectors A = 3ix + 4iy and B = 7ix – 24 iy a. What is their dot product? b. What is…

A: Given : A=3ix+4iy, B=7ix-24iy.

Q: Find the dot product for the pair of vectors. i+ 4j, 7i - j O -3 3 11 Question 13 (1 point) Listen…

A: FIND THE VECTOR DOT PRODUCT AND ANGLE BETWEEN TWO VECTORS

Q: A new landowner has a triangular piece of flat land she wishes to fence. Starting at the west…

A:

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: Given: 6j, -4i

Q: Q.5) Determine and what is the differences between the two results. Also prove that is orthogonal to…

A: We have to find the difference between the vectors A→=-i^+8j^+4k^ and B→=i^+18j^-6k^. Also, prove…

Q: (a) b B M D 0 C a A In the above diagram, OA= a and OB = b. C lies on OA where OC= the midpoint of…

A:

Q: Express the following vectors in Cartesian (component) form. a) f has magnitude 20 and direction…

A: Solution:-

Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

A: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

Q: Compute the following cross product. Then make a sketch showing the two vectors and their cross…

A: We need to evaluate the following cross product -2k×5j

Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the…

A: Consider the given question,

Q: Find two unit vectors that are perpendicular to both  j + 5k  and  i − 2j + 5k.  (Enter your…

A: The given vectors are u=0i+j+5k   and  v= i-2j+5k. Compute the cross product as follows.…

Q: 1. (a) Calculate the dot product of the two vectors (b*) Find the value for c for which 2 and [2] C…

A: Calculating the dot product of two vectors

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: Calculate the angle 0 between vectors a and b when a = i – 2j + 2k , b = 2i + 3j + k %3D

A:

Q: Find two unit vectors that are perpendicular to both j + 5k and i − 4j + 3k. (Enter your…

A:

Q: Find the following for the vectors u = - 9 i-2j + v2 k and v = 9 i+2 j- v2 k. a. v•u, v|, and u b.…

A: Let a→ = a1i^ + b1j^ + c1k^ and b→ = a2i^ + b2j^ + c2k^ two vector. Then, a.b = a1a2 + b1b2+c1c2 a…

Q: Consider the vectors a = 4 i+ 8 j-8k, b = 2 i +k and c = 4 j-5k. Are the vectors a and b+c…

A:

Q: Convert the following vectors to their equivalent vectors in cylindrical and spherical coordinate…

A: The components of the spherical vector are r,θ,ϕ Which are related as r=x2+y2+z2…

Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

A: Given that, u=a1i+b1jv=a2i+b2jw=a3i+b3j

Q: Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i-…

A: We have to find whether the given vectors are parallel, orthogonal, or neither by using the dot…

Q: Find the following for the vectors u = 6i + 9j + v2k and v = - 6i – 9j – V2 k. a. v•u, v, and u b.…

A: We have to solve

Q: Find the acute angle between the two vectors A = 2a, +a, + 3a, and B = ax – 3ay + 2a, by using the…

A:

Q: Q1) Sketch the vectors in a,b,c, and d using the provided figures A) a. u + v b. u + v + w C. u - v…

A:

Q: If v = 5i + 6j and w = 10i + 12j, find proj,v. Then decompose v into two vectors v, and v2, where v,…

A: