11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21 +ỉ -k and h =i +k in 3D [A:31

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

A:

Q: The norm of the vector v= - i+10j-8k is ||v||=, (Round your answer correct to 3 decimal places)

A:

Q: 3. Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v = 4i…

A:

Q: C A

A: We use Triangle law

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

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: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

A:

Q: Consider the two vectors A = A,i + Ayj and B = B,î + Byj. In cross product, %3D %3D ixî = j xj = 0,…

A: We have given two vectors A→=Axi^+Ayj^  and  B→=Bxi^+Byj^ i^×i^=j^×j^=0i^×j^=k^, j^×i^=-k^   Find…

Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: What is the resultant of vectors a and b? ( A ) GL B

A:

Q: Given the vectors u = (2, -2, 3) and v = (-3, 2, – 1), calculate the vector projection of u onto v…

A:

Q: Consider the vector v = (x, 2) in R2. If you rotate the vector by 90-degrees counter-clockwise, then…

A:

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

A: Given query is to find the angle between the vectors.

Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

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: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

A:

Q: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

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: The projection of the vector ( i-j+5) onto the vector 2 i+ j + 4 k is

A:

Q: Consider the vector i 3, and let V 4 = span(ï) C Rº. %3D %3D 5

A: Given: Let the vector V→=12345 and V= span(V→)

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u3(-12,0,6)…

A:

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

A:

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

A:

Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

A:

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

A:

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

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: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

A:

Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: 16. Consider this regular octagon. If AB =d and BC =v, express each %3D vector in terms of u and v.…

A: Considering OD on x-axis. Angle at center O made by any side of regular octagon is 45degrees.

Q: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: i +j +k andi – j -k.

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

Q: Consider the four vectors X1 = (0, 0, 0)', X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)'. %3D…

A:

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

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

A:

Q: 26. Find a unit vector whose representations are perpendicular to the plane containing PQ and PR if…

A:

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

A:

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

A: To find the normal unit vector perpendicular to A and B

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

A:

Q: (a) Calculate the dot product and angle between two vectors, where u 7j– 2k and v = (1,2,3).

A:

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: Using the vectors from the previous problem, find the projection ul of v onto the vector u and find…

A: We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product…

Q: b) Show that the vector w = u – proj,u is orthogonal to proj, u

A: The expression for the vector projection of u onto v is: projvu=v·uv2v Given: u=3,4,0 and v=-2,3,-6…

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^