Find the distance between u and v and determine whether u and v are orthogonal, parallel, or neither u = (0, 1, 0), v = (1, –2, 0) u = (0, 3, -4), v = (1, -8, -6)

Q: Find the distance between u and v. u = (0, 1, 2), v = (4, 1, -1) d(u, v) = ||

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Q: Express the vector P, P2 in the form v = v, i+ v2j + v3k if P, is the point (- 7, - 3,1) and P2 is…

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Q: Find vectors u and v whose initial and terminal points are given. Determine whether u and v are…

A: The u vector can be computed as: u=6-1i+11-1ju=5i+10j

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find 1 the area of the parallelogram determined by u…

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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: Consider the vectors (2, 1, 0, 2], [3, 1,0, 1], [1, 1, 0,-1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Find the distance between u and v. u = (-1, 0, 0, 4), = (0, 0, 4, 4) V =

A: Distance between two vectors can be calculated by subtracting the vectors and taking the square root…

Q: Determine whether u and v are orthogonal, parallel, or neither.

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Q: Express the vector u = (1,-8,0) as linear combination of the vectors u, =(4,5,0) and u, = (7,6,0)…

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Q: Use vectors to determine whether the points are collinear (0, -2, -5), (12, 7, 1), (8, 4, –1) The…

A: Given: (0,-2,-5) , (12,7,1) & (8,4,-1) are three points.   To Check : The given points are…

Q: Find u × v and show that it is orthogonal to both u and v. u = v =

A: Given u→=-1,0,7v→=8,-4,0

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Find vectors A and B such that A is parallel to (2, 1,-1), B is perpendicular to (2, 1, -1) and A +…

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Use vectors to determine whether the points are collinear. (4, −2, 7), (−2, 0, 3), (7, −3, 9)

A: Formula: the vectors a, b and c are collinear if detabc=0.

Q: Find the distance between u and v.u = (0, 1, −1, 2), v = (1, 1, 2, 2)

A: Given:U=(0,1,−1,2)V=(1,1,2,2)To determine the distance betweenU and V.

Q: Use vectors to determine whether the points are collinear. (0, −2, −5), (3, 4, 4), (2, 2, 1)

A: A(0, −2, −5), B(3, 4, 4) & C(2, 2, 1) be the given points. Now vector joining the points A and B…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: Find the cross product a ✕ b. a = (7, 0, −2) , b = (0, 6, 0) Verify that it is orthogonal to both a…

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Q: Find the distance between u and v. u = (1, 0, 2), v = (1, 4, –1) d(u, v)

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Q: Determine whether u and v are orthogonal, parallel, or neither.

A: We need to  Determine whether u and v are orthogonal, parallel, or neither.

Q: Find orthogonal projection of u=(-1, 2, 5) in the direction of v=(3, 1, -2).

A: find the orthogonal projection of u=-1,2,5 in the direction of vector v=3,1,2 it is known that…

Q: Use vectors to determine whether the points are collinear. (0, 0, 0), (1, 3, −2), (2, −6, 4)

A: Given:A0,0,0B1,3,-2C2,-6,4

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

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Q: Use vectors to determine whether the points are collinear (3, 4, −1), (−1, 6, 9), (5, 3, −6)

A: we have to use the vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,-6) are…

Q: Let a be the angle between the vectors u=(-3,4,0) and v=(-4,3,0). Then

A: Given, the vectors u=(-3, 4, 0), and v = (-4, 3, 0).

Q: Determine whether u and v are orthogonal, parallel, or neither.u = (0, 1, 0), v = (1, −2, 0)

A: Now dot product is, Since the dot product is not zero, therefore u and v are not orthogonal. Now…

Q: Find the distance between u and v.u = (1, 2, 0), v = (−1, 4, 1)

A: Distance between the two points :P1x1,y1,z1P2x2,y2,z2d=x2-x12+y2-y12+z2-z12d→distance

Q: Find the distance between u and v. u = (3, -3), v = (-3, 3) d(u, v) :

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Q: Find the values of x such that the vectors and are orthogonal

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Q: Use vectors to determine whether the points (3,4,-1), (-1,6,9) and (5,3,4) are collinear.

A: The points (3,4,-1), (-1,6,9) and (5,3,4)

Q: Find the distance between u and v. u = (-2, -1, 1, 2), v = (-1, –1, 2, 2) d(u, 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: Determine whether u and v are orthogonal, parallel, or neither.u = (0, 3, −4), v = (1, −8, −6)

A: u = (0, 3, −4), v = (1, −8, −6) We need to determine whether u and v are orthogonal, parallel, or…

Q: Write v as a linear combination of u,, u2, and uz, if possible. (If not possible, enter IMPOSSIBLE.)…

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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 v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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Q: u

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Q: Find orthogonal projection of v=(3, 1, -2) in the direction of u=(-1, 2, 5).

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Q: Determine whether u and v are orthogonal vectors. 1. u = (6,1, 4), v = (2, 0, -3) 2. u= (0, 0, -1),…

A: Two vectors a and b are orthogonal if a.b = 0 1.) Given u = (6 , 1 , 4)v = (2 , 0 , -3) Then u.v =…

Q: Let a and b be real numbers. Find all vectors ⟨1, a, b⟩ orthogonal to ⟨4, -8, 2⟩.

A: Given  a and b are real numbers. (1,a,b) is orthogonal to (4,-8,2).

Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…