5. For each pair of vectors, calculate proj„u and the vector component of u orthogonal to v. (a) u = (3, 1, –7), v = (1,0,5) %3D

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

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

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: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  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: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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: 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: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

A:

Q: Find the vector component of v = (4, – 1, 7) alongb = (1, 2, –2) and the vector component of v…

A:

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

A:

Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

A:

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

A:

Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

A:

Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

A:

Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

Q: (2) For the vectors ä = (-1,3, 4) and 5= (-2,2, 0) calculate the following: (a) ãoË (b) ä x b (c) A…

A:

Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

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

A:

Q: d a vector orthogonal to both u and v.

A:

Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: For which value of k the two vectors u=(3,3,k) and v= (-4,8,1) are orthogonal? *

A:

Q: 1. Plot the following vectors using arrows on an xy-graph: -- (}). v-[+]. 1 u = V = 2u, u+v. Is…

A:

Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

A:

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: What is the magnitude of a vector joining two points P(x1, y1, z1) and Q(x2, y2, z2)?

A: The two points  are : P(x1, y1, z1) and Q(x2, y2, z2). As the vector is directed from point P to Q ,…

Q: B. Find a vector has length 10 in the direction of vector V=.

A:

Q: Find a unit vector orthogonal to both u and v. u = -3i - 2j - 5k li 1 3i+ -j + 4 10 V = - 2

A: To find A unit vector orthogonal to both u and v

Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

A:

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

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

A: