Let A=(0,−3,1), B=(−2,3,2), and P=(k,k,k). The vector from A to B is perpendicular to the vector from A to P when k = ?

Q: Find the vector z, given that u = (3, -2, 5), v = (0, 2, 1), and w = Z= z = −u + 4v + 1 _W 2 (-6,…

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Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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

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Q: Let A=(−3,−5,0), B=(−2,−2,2), P=(k,k,k). The vector from A to B is perpendicular to the vector from…

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Q: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). Write v in terms…

A: Let v be the vector from initial point P1 = (4, -5), to terminal point P2 = (4, 3). To write v in…

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩. .   z = −u + 3v +…

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Q: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: Find a unit vector u in the direction of the vector from P1(1, 0, 1) to P2(3, 2, 0).

A: Concept: Unit vector is a quantity which has a magnitude as 1and as well as direction, it is also…

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…

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Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: Find r so that the vector from the point A(1,−1, 3) to the point B(3, 0, 5) is orthogonal to the…

A: The vector from the point A(1, -1, 3) to the point B(3, 0, 5)            Is orthogonal to the vector…

Q: Let j = | and ü .Write j as the sum of two orthogonal vectors, it -2. %3D an {u} and ¤2 orthogonal…

A: Given:- →y=-69  →u=5-2

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: (€) Let a = and b = be two vectors. What is al2|b|? - |a · b|? ?

A: Given vectors are, a=2-10  and b=-111 The modulus of the given vectors will be, a=22+-12+0…

Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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Q: For any vector u, v E R³, v. (uxu) (uxu) = 0.

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Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: Let v = ( 1, 2 ), Find a vector w with the same direction as v such that || w || = 7.

A: Let v=1,2 Then,  v=12+22=5 The unit vector in the direction of v is, v=vv=1,25=15,25

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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

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Q: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: find the sum of vector AB and CD where A (1,-1) B (2,0) C(-,3) D(-2,2)

A: Let A (1,-1) B (2,0) C(-1,3) D(-2,2) be the given vector. Of course here in the problem   "-1"is…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

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Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Let v be the vector The vector of length 3 in the opposite direction as v is 2 Select one: a. -2 O…

A: Vector v  = (1,2,-2) opposite direction to  given vector can be find as -v (-1,-2,2)

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: Given the points A(-6, 4) and B(-3, 5), express | the vector AB in terms of i and j.

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Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: For the vectors u (1,0, 1) and v (0, 2, 1), u x v = %3D O A. (1, 2, 0) O B. (1, 2, -2) OC. (2, 1, 2)…

A: Given. The vectors u = 1, 0, 1 v = 0, 2, 1 We have to find u×v

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: For any vectorV and unit vector U parallel to V , then D-

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Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: Let v be the vector from initial point P1 = (4, -5) to terminal point P2 = (4, 3). Write v in terms…

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Q: Let u and v = .A vector orthogonal to both ú and v is

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Q: Let A=(3,3,−4), B=(0,−2,−2), and P=(k,k,k). The vector from A to B is perpendicular to the vector…

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Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

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Q: Let v be the vector from initial point P, to terminal point P,. Write v in terms of i and j. P1 =…

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Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

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Q: Let P = (-2,0, 5), Q = (3, 1, 1), and R = (0,0, 4) and define a = PÓ and b= PR. Find (b) A vector…

A: a  =3+2,1-0,1-5       =(5,1,-5) b =(0+2,0,4-5)    =(2,0,-1)

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector