9. Which vector is the orthogonal projection of v = onto W = span 4. 2 V3 V6 V3 V6 O 1 /1\

Q: If a vector u is orthogonal to vectorsx and y then u is orthogonal to the vector x + y.

A:

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

A:

Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

A:

Q: Suppose v, w, z are vectors in R". Show that if r and y are linear combinatio: v, w, and z, then r+…

A: Linear combination of the vectors

Q: 6. If u,v, and w are three vectors in R', describe their linear span.

A: 6. If u,v and w are three vectors in R7, we have to describe linear span.

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.

A: (a) find the projection of u onto v and (b) find the vector component of u orthogonal to v.…

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: onow that the v ectors 2 3 do not span R' by giving a vector not in their span.

A:

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

A:

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: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: If a vector u is orthogonal to vectors x and y then u is orthogonal to the vector C1X – C2y. Select…

A:

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: What is the unit vector oppositely directed to 4?−5?−5??

A: Topic:-  vector algebra

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: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&amp;V…

Q: Show which of the following are orthogonal vectors v, = 18] V2 = %3D Or = Liel Uz = 18

A: Check the dot product of given vectors are zero or not, if zero the orthogonal otherwise not

Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

A:

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

A:

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

A:

Q: Find the projection of vector A=(6,7) along vector B=(1,4).

A:

Q: 10. Given two vectors u =6,2] and v = [-2,1), determine the projection of u on v.C %3D %3D

A:

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: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Sketch the vector b = &lt;3, 4&gt; based at P = (−2, −1).

A: Sketch the vector b=&lt;3, 4&gt; based at P=(−2, −1).

Q: 10) Find two vectors of norm 1 that are orthogonal to the vectors u = and

A: Consider the provided question, u=12-23 and v=2134 Let w=ABCD be such a vector,Then, w·u=0…

Q: Find the length of the vector. v = (0, 9)

A:

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: Find the unit vector u in the di rection of the vector v=2(2, 1, 2).

A:

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

A:

Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

A:

Q: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

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: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Suppose a vector y is orthogonal to vectors u and v. Show that y is orthogonal to the vector u + v.…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Find the unit vectoru in the di rection of the vector v=4 (2, 1, 2). 1 u = u = В. 1 12 u = 1 u = 15…

A: v=4(2,1,2)v=(4*2,4*1,4*2)v=(8,4,8)Magnitude of vector|v|=(8)2+(4)2+(8)2=64+16+64=144=12unit vector u…

Q: Which vector is the orthogonal projection of v = 0 onto W = span -2 °() V3 V6 3 V6

A:

Q: Find the weighted Euclidean distance between the given vectors. -- - - u = 3 with weights w = d(u,…

A:

Q: Find a unit vector that is orthogonal to both u and v.      u = ⟨−8, −6, 4⟩,          v = ⟨10, −12,…

A: Consider the following vectors: u=-8,-6,4v=10,-12,-2 A vector orthogonal to both u and v is the…

Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

A:

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: Find the length of the vector v = (1, 1, 7).

A: Given : v = 1, 1, 7

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

A:

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…