Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on cartesian coordinates does this vector parallel to?

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 a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, –1) V =

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Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

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Q: Find the unit vector in the same direction as the vector u = [8, –7].

A: When you divide a vector by its magnitude you get an unit vector along its direction.

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a rectangular…

A: Question- Compute the resultant of the position vectors for the points (2,4,3) and (1,-5,2) of a…

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

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Q: Find a vector equation for the line through the point (-3, –1, 8) perpendicular to the vectors ū =…

A: Vector equation of the line passing through point (a,b,c) and perpendicular to vectors u→ and v→ is…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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

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Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

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

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Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

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Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

A: We will solve the problem

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, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

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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: Find the unit vector in the same direction as the vector u = [-8, 6, 7].

A: Given,         The unit vector in the same direction as the vector u=-8,6,7.

Q: Express A = (3, 1, – 1) as B+ C, where B is parallel to the vector (1,4, 2) and C is perpendicular…

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Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

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

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

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

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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: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Find the vector with length V17 and same direction as i= (7,0, –6).

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: For the vectors u = (- 3,5) and v = (- 5,2), calculate proj,u and scal,u.

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

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: Find a unit vector which is perpendicular to both đ = (1, 1, 0) and b = (-2, 3, 0) Answer:

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

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

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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

Q: Determine whether the vectors {(1,-1,2).(-1,1,2).(0,0,1)} span R3. If they do, give the linear…

A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

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

A:

Q: Find a unit vector that is perpendicular to both ū = (1, 2, –2) and v = (2,1,2). Answer:

A: The vector which is perpendicular to the plane containing vectors u and v can be calculated by the…

Q: Find a unit vector u that had the same directions as the vector v= (-3,3,-2)

A: Use the basic property of unit vector

Q: Find the orthogonal projection of the vector a (-9,-8, 7) in the direction of the (-3,-5,-2). 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: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry

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

A: Topic = Vector