Consider the points A, B, C, D where coordinates are respectively (1, 1, 0), (-1, 1, 0), (1, – 1, 0), (0, – 1, 1). Find the direction cosines of AC and BD and calculate the angle between them.

Q: Given the following points: P(3, - 1, 5) , Q(3, 3, 6) and R(2, 3, 7) forms the triangle. Find the…

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Q: Let →a=⟨2,5⟩a→=⟨2,5⟩ and →b=⟨0,k⟩b→=⟨0,k⟩.Find k so that →aa→ and →bb→ will be orthogonal (form a 90…

A: For given two vectors, the condition for orthogonality is that there dot product is equal to zero.

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Let a = 2i +j- 2k and b = 2i + 4j + 3k %3D (а) Determine whether a b and a +b are orthogonal,…

A: To fins a) and  b)

Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectangular coordinate system (x,y,z) SCS- Spherical coordinate system ρ,θ,ϕ CCS- Cylindrical…

Q: Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v…

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Q: Let A = (-1,2, 0) and B = (2, – 1, 3). Determine the following: (а) 2A В (b) angle between A and B…

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Q: Let u = (3, 4) and v = (8,6). %3! a) Calculate u · v, ||u|| and ||v||. b) What is the cosine of the…

A: Given that        u= (3,4) and v=(8,6) We have to find       (a) u.v , ||u|| and ||v||    (b) the…

Q: If the position vectors of the points A, B, C, D are a = i + j + k, b = 2i + 3j, c = 3i + 5j − 2k, d…

A: Consider the vectors: a=i+j+k……1b=2i+3j……2c=3i+5j-2k……3d=k-j……4

Q: Find the direction cosines of u and demonstrate that the sum of the squares of the direction cosines…

A: we find direction cosine with x, y and z axis..

Q: Plot the point (r, theta) = (6, 181) %3D Clear All Draw: Dot

A: we know that r= 6 will give a circle of radius 6 and center at originand angle θ varies from 0 to…

Q: Let u = (3, 4) and v = (8,6). (a) Calculate u · v, ||u|| and ||v||. (b) What is the cosine of the…

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Q: Find the angle of intersection α of two cardioids r1=1+cosθ and r2=1−cosθ.

A: Consider the Figure:

Q: For this question, how would I write the V in terms of i and j with the given direction of theta?

A: We have to write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are…

Q: if theta is the angle between the two vectors, v, and w, find the measure of angle theta in degrees,…

A: Use given vectors find angle between them

Q: If v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w, then tanθ = ? v and w are…

A: Given  v × w =4i −j +k, and v⋅w=5, and θ is the angle between v and w  Now we have to find tanθ as…

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: Suppose u = (1,1,–2), v=(3,-2,1), and w =(0,1,-5). Find: %3D (a) The cosine of the angle between u…

A: We will answer the first three subparts of this question as per our guideline. Please resubmit the…

Q: Suppose that v and w are unit vectors. If the angle between v and i is a and the angle between w and…

A: Vector is a physical quantity having both magnitude and direction . Dot product of two vector A and…

Q: In the diagram below, the coordinates of figure CAT are C (1.3). A (2, –1). and T (4, –1).| Give the…

A: concept:  Whenever we rotate a point about 180° around origin (0,0) then their sign changes. Like…

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle 0 between the vectors v and w.…

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Q: Let →a=⟨3,−1⟩ and →b=⟨−4,k⟩ Find k so that →a and →b will be orthogonal (form a 90 degree angle).…

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Q: Suppose the vector t has magnitude 48 and makes an angle of 239° with the positive x-axis (measured…

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Q: Let 3. 2 -1 X= y = 3. 3 (a) Find x), yl, and the angle between x and y.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: I am attaching image so that you understand each and every step.

Q: 3. Find the angles a, ß,y, which the vector Á = 3î – 6î + 2k makes with the coordinates axes and…

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Q: Let y = 3 -3 (a) Find |x, yl, and the angle between x and y.

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Find the component form of u + v given the lengths of u and V and the angles that u and v make with…

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Q: Let →a=⟨−4,−5,−2⟩and →b=⟨1,−1,5⟩ In Radians, find the angle between the vectors

A: Angle between vectors

Q: Let a = (- 3, 2) and b = (2, – 5). Find the angle between the vector, in degrees.

A: Given:           a→=-3, 2 and b→=2, -5 We know that the dot product of two vectors is defined as…

Q: Find the angle in degrees between u = (1, 2, 0) and v = (1, -2, 1)

A: Given, u=1,2,0v=1,-2,1 The formula for finding the angle between the two vector is, cosθ=u→·v→u→v→

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle e between the vectors v and w.…

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Q: Calculate the latitude and longitude angles for the following Cartesian coordinates.…

A: To calculate the latitude and longitude angles of given Cartesian coordinates. For first coordinate…

Q: Find the angle between u=3i+2j and v=-4i

A: Given,          The two vectors are u=3i+2j and v=-4i.

Q: Show answer clearly.

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Q: Let a = (- 2, 4) and b = (1, 3). Find the angle between the vector, in degrees. Round your answer to…

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Q: Match each point in polar coordinates to the points A, B, C, and D. A(3, E).B(3, #).C(3, – }).D(-3,…

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Q: Let →a=⟨−2,−1⟩ and b→=⟨0,-5⟩. Find the angle between the vector, in degrees.

A: We can find the angle between the vectors as below.

Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

A: topic - vectors

Q: 6- 12 -8 2 4 P.

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Q: Let ā = (4, 3) and b = (– 4, 4). Find the angle between the vector, in degrees.

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Q: For vectors ū = (1,-5,2) and v = (3, 1,-4), calculate the following: a) ū• i b) the angle between ū…

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Q: What is the degree AND direction of rotation that takes AQRS to AQ'R'S'? R

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Q: In the methane molecule, CH4, each hydrogen atom is at a corner of a regular tetrahedron with the…

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Q: Let ä = (– 3, – 2) and 5 = (1, k). Find k so that ä and b will be orthogonal (form a 90 degree…

A: Two vectors a→ and b→ are orthogonal if their dot product is zero, because both the vectors are…

Q: Let ā = = {– 1, k). (- 5, 4) and b Find k so that ả and b will be orthogonal (form a 90 degree…

A: the solution is given below

Q: Let →a=⟨−5,−3⟩ and →b=⟨3,k⟩ Find k so that →a and →b will be orthogonal (form a 90 degree angle).…

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Q: Let a = (4, 1) and b (4, – 1). %D | Find the angle between the vector, in degrees.

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