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 A to P when k =?

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

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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: Write the vector u=<2,-3,1> in the form v+w, where v is a vector parallel to the vector…

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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 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: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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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: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

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: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

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: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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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: Let v be the vector from initial point P, to terminal point P2. Write v in terms of i and j. P,…

A: We will use the fact that a vector is determine by the initial point and final point as given in the…

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: Let v be the vector from initial point P1 = (2, -1) to terminal point P2 = (5, -3). Write v in terms…

A: Given that v is the vector that has initial point P1 = (2, -1) to terminal point P2 = (5, -3).  we…

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

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Q: Let A, B,C be three points not lying on the same straight line. a. Which set of points P is…

A: Here given A, B, C be three points not lying on the same straight line that means these points not…

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 v be the vector from initial point P1 = (-4, -4) to terminal point P2 = (6, 2). Write v in terms…

A: Given initial point P1=-4,-4 and terminal point P2=6,2. Given points can be written as: P1=-4i-4j…

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v - u) -…

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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: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

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, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: 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…

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Q: Let v be the vector from initial point P1 = (-4, -4),to terminal point P2 = (6, 2). Write v in terms…

A: Initial point is P1=-4, -4 & terminal point is P2=6, 2.

Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

A: The given vector is u=[1,0,-1] and v=[-2,1,2]

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

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 = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

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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: Linear algebra

A: From the given information:Let,

Q: Give the vector equation of the line passing through P and Q.P = (1, 1, 0), Q = (1, 0, 1), R =…

A: P=(1,1,0) and Q=(1,0,1)we have to find vector equation of the line passing through these points

Q: IH A and B are any two vectors in V, prove that (A- B) x (A + B) = 2(A X B).

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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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…

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

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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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