Use the scalar triple product to determine whether the points A(1, 3, 2), B(3, -1, 6), C(5, 2, 0), and D(3, 6, -4) lie in the same plane.

Q: Find the of A ABC Where the area vectors AC1,-1,1), B(2,1,1) and are cl-1,1, 2).

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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.…

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Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 6v

A: Given: The vectors u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: Use the scalar triple product to detemine whether the points A(1, 3, 2), B(3.-1.6), C(5, 2, 0), and…

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Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…

A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w

Q: Let x and y be vectors in the R³. Suppose that x is a scalar product of 2 and the vector y. Prove…

A: x and y are vector in R3, x is scalar or dot product of 2 and y vector,  it means x = 2.y,

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 ä xb and bxå. Confirm that the cross product is orthogonal to each vector. ā=[4, –3, 5],…

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Q: The scalar product 0v is 0.

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Q: Find the scalar and vector projections of b onto a, where a = (2, −2, 1) and b =  (IMAGE)

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

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Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Find the scalar and vector projections of b onto a. a = b =

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Q: Use the triple scalar product to find the value of p that makes the three vectors below coplanar.…

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Q: Find the scalar and vector projections of b onto a. a = (1,6), b = (-7, 1) compab = projb =

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Q: The dot product of u = (3, 5, 2) and v = is equal to the scalar product of p = 31 - 5j + 2k and q =…

A: The component representation of a vector u=ai+bj+ck is  u=<a, b, c>. So the vectors u and v…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar -4w.

A: It is given that  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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Q: In each part, use a scalar triple product to determine whether the vectors lie in the same plane.…

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Q: Find the scalar and vector projections of b onto a. a = 3i - j+ 6k, b = j+k = j+ k compab = projąb =

A: Here we find the scalar and vector projection of b→ onto a→where a→=3i∧-j∧+6k∧ , b→=j∧+12k∧

Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: Verify that (λv) · w = λ(v · w) for any scalar λ

A: For any vectors x,y we have x·y=xycos θ where θ is the angle between x and y.

Q: 6) Use the scalar triple product to verify that the following vectors are coplanar: ü = i + 53 – 2k…

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Q: Write a scalar equation of each plane, Given its vector equation [x, y, z] = [7, -3, 4]+s [1, -2,…

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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: Find the scalar and vector projections of b onto a, where a = (-1, 1, 2) and b = (-2,7,2). 1. comp,…

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Q: Find the magnitude of the scalar multiple, where u=(2,0) v=(-3,6) ll-2vll

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Q: Find the scalar and vector projections of b onto a, where a = (1, 2) and b = (-4, 1). 1. comp, b 2.…

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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 the scalar and vector projections of b onto a. а - (-4, -3), ь - (6, 0) compab projąb

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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 scalar AND vector projections of a onto b where a=(0,1,-2) and b=(-1,0,3)

A: Given , a = (0,1,-2) and b = (-1,0,3).

Q: 6. Use the scalar triple product to determine if the points A(1,3, 2), B(3, –1,6), C(5, 2,0), and…

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Q: Find the scalar and vector projections of b onto a. a = 3i − j + 4k,    b = j + (1/2)k   compab =…

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Q: Show with the help of the calculation rules for the scalar product for vectors ||x – 2 y|| = ||x||2…

A: The property used here are b2=b·b x·y=y·x cx·y=cx·y=x·cy Consider the left hand side of the given…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 5v.

A: Consider the given vectors u=2i-5j , v=-3i+7j , w=-i-6j

Q: u

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 3v - 4w.

A: Given  u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. We need to find the specified vector or scalar…

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: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar lul.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: u  Solution: Magnitude of a vector is…

Q: Calculate the scalar triple product u· (v x w), where u = (1, 1, 0), v = (2, –3, 5) and w = (4, –1,…

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Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

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 scalar and vector projections of b onto a, where a = (1,2) and b = (-–9, 1). %3D 1. comp, b…

A: We have to e the magnitudes of thr given vector first.

Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: Find the scalar and vector projections of b onto a. (4, 7, -4) ь 3 (3, -1, 1) a

A: a=4, 7, -4, b=3, -1, 1 1. Scalar projection of b onto a is Proj ba. Proj ba=b·aa          =3, -1,…