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 perpendicular to both a and b.

Q: Find a unit vector that is orthogonal to both u and v for u = and v = .

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

A: Given the points P1=3,-1 and P2=-2,5.   The vector is, v=P1P2→=-2-3,5--1=-5,6

Q: Let v be the vector from initial point P1 = (2, -5) to terminal point P2 = (-6, 6). Write v in terms…

A: Given, The initial point is P1 = (2, -5) to terminal point P2 = (-6, 6).

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: Let v be the vector from initial point P1 = (-1, 6) to terminal point P2 = (7, -5). Write v in terms…

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Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

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 the vector from initial point P1 = (-7, -4),to terminal point P2 = (0, -2). Write v in…

A: Vector u from (a,b) to (c,d) is (c-a,d-b) or  (c-a)i+(d-b)j

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: 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: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

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

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Q: Let v be the vector from initial point P1 = (-7, -4) to terminal point P2 = (0, -2). Write v in…

A: To write the vector v in terms of i and j.

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: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

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

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

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 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 unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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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: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

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: Let the vector be x = (5,6), determine its coordinates relative to the base B = {(1,1),(-1,2)}}

A: Introduction: When a basis is provided, one can represent a vector belonging to the precise vector…

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Use the vectors u = (4, 4), v = (-7, 2), and w = (4, –1) to find the indicated quantity. (u · v) –…

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Q: Find the vector z, given that u = (3, 2, 9), v = (2, 2, -1), and w = (4, 0, -4). %3= z = u - v + 2w

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Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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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 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: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

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Q: Let v be the vector . The vector of length 5 in the opposite direction as v is Select one: a. 5 -5…

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

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Q: Find the component of V, |V|= V5 in the direction of a vector from A(0,0, 4) to B(2,5, 0).

A: The vector joining the points A0,0,4 to B2,5,0 is given by, AB→=2-0i^+5-0j^+0-4k^=2i^+5j^-4k^ The…

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: Linear algebra

A: From the given information:Let,

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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